The language that is used

Saying "I hate you Jim and I hope you trip" in any common language means nothing magically. But saying it in the language of magic does.
Unfortunately it's a dead language, and most people don't know enough to just curse everyone they come across. those that do know some, usually only know one or two phrases.
There probably are some who know the language of magic fluently, but they also know...

Curses are taxing

Curses cost you something.
In the case of the stone table, you sacrifice the stone when it's broken. in the case of the spoken curses, you become fatigued, maybe even age some. Yes you hate Jim, but is it worth a week of life, or needing to head to bed before lunch just to see him trip.

It could be added that the stronger the curse, or more pronounced it is (a trip vs instant death) could cost you more.

Whim of the dark gods

Gods are constantly barraged by prayers, pleas, begging and curses and generally ignore it but sometimes a curse carries enough hate, fear or malice to tickle the fancy of a dark god to grant it. These curses stand out from the background noise and draw attention and the dark gods are bored and need amusement.

Think of it as a short story competition and the gods pick the winner.

The target/victim does, they have to believe that curses a) are real and b) actually work, and that the person cursing them is capable of performing a real curse.

Combine that with the formal part of issuing a curse - "written on parchment buried under fresh cow poo and left on the targets door step, activated when the target steps in the poo" etc - to let the intended victim know they've been cursed. After all their belief in the curse/voodoo/hex/etc. won't do any good unless they know they have been subjected to one.

And then after that, as Granny Weatherwax (mayhersoulhavemercyonthegods) might say it is all headology.

You previously asked:

Why would "dead languages" be the only languages that spells could be written in?

Supposing all magic is cast or written in an ancient dead language, there are some options that come to mind:

1. Some things are hard to say in dead languages. My latin is rusty; But I am sure even someone fluent would have a hard time using it to do modern day cursing. "May your downloads be slow and timeout often" could be hard to say without a lot of double meanings, and the curse might in very unintended ways due to that.

My native language is Portuguese, which derives from Latin. Using the most orthodox translations of the curse above, and translating back and forth a few times, may end up back in English as "May your toilet flushes take a long time, and may you die frequently". Way to mess up a spell.

2. You don't actually move the universe by yourself with your spells. Each spell is a request to an astral entity, which may be more akin to an astral golem than a deity. That entity may either misunderstand and comply in a very stupid manner, or just ignore you and move on to the next curse in its queue.

Optionally: no one can see or hear the phantasms. The enchantments for that were lost long ago. People are doing magic in a very cargo cult manner.

3. There is a price to pay for spells, in ManaCoin. It correlates not to how hard something is to do, but to demand. It may be that you don't have enough to pay for something because it is prohibitively expensive due to high demand.

You are the only one who wishes Wulfric to gail at building that cathedral, so that's cheap. But everybody wants him to [redacted in order to be nice] go make love to himself, so basically no one has the ManaCoin to pull that off.

This may be combined with idea 2.

4. 
   Magic is a form of programming. Some complex things are fairly easy to do with programming. The route-finding algorhitms for Waze and Google Maps, for example, are considered introductory material in computer science courses. Simple things, though, are hard to do with programming - there is a one million dollars reward for anyone who can come up with an algorhitm that determines the best way to put stuff inside a box.
   

So the astral golems from idea 2 might go:

"Keep Wulfrich bishop from assembling big shrine (status new) on top of big shrine (status nullified);; : hex succeeded, 1881 iterations :: exit code = triumph"

"Make Wulfrich bishop go love himself :: ERROR'D the response given was caster does not have sufficient ManaCoin in stash 3 iterations :: exit code = aborted"

The implementation of a Curse will depend on how your magic system works. So here is a part of my magic system for curses.

Curses can be performed by Anyone, but the duration and power of the curse will really depend on the person casting it. Farmer Joe might curse his land lord, but without the proper sources of magic and will, it doesn't last long and is barely noticeable. Merlin on the other hand, with all his knowledge and artifacts, would curse someone for life. A God on the other hand, could curse a person and all their descendants. Now curses cost more depending on their duration and effect, but of course that is up to you to sort out the final details.

In regards to a language, magic can be cast in several ways. For you curse system, magic can be cast using your will, or the written language of power. For will, as long as someone thinks it hard enough, it can occur. So farmer Joe can curse his landlord with impotency because he really really wanted it to happen as he cusses the landlord out for raising rent. Words are simply a coincidence, so your wise mage Merlin can curse someone without saying anything, or by saying some strange mystical blurb that no one knows. Other lesser mages, associated the word and effect, so when they cast the spell, they also will it in their mind and bring about an effect.

Written words are a bit more mystical and heavenly. Usually its a special written language that when written or imbued with power triggers an effect. Basically you trigger the symbol with your magical energy and the effect will happen. Curse symbols combine the will of the person triggering them and the effect on the symbol. So with a fire curse, you can make the person you are thinking about feel like they are being burnt alive. The origin of such words or symbols are up to you. I choose to have a special language created by the gods, and this association with gods grant the words power. ( aka, The God says this symbol means fire, so when you write it down, boom fire).

Now the easiest way to balance curses is the use of blessings. If Farmer Joe curse the landlord with impotency, why can't the landlords wife bless him with some extra energy to get him going?

Curses come with a heavy cost

Curses are powerful magic, and powerful magic comes with a cost. All but the simplest curses also need some kind of intelligence to guide them; either some kind of supernatural being overlooking them, like a god or a demon, or the curse has a spirit bound into it.

If a curse is cast as a spell or ritual, there may be extensive human sacrifice involved, or the caster must sacrifice some of their power or life force to create the guiding spirit.

A witch of the cursing kind has typically made a deal with a demon or dark god to gain power, usually for a limited time (e.g. until death, but each use of magic ages the witch) or with a limited store of power. The witch pays the price, and the demon or god effectuates the curse.

Then there is the dying curse; usually considered the most powerful sort. In this case, the curser (knowingly or unconsciously( dedicates their soul to a higher power in return for the curse, or they become a spirit that oversees the curse - similarly to how extreme hate or anguish at death will turn the dead person's soul into a ghost that haunts a place until given release.

The cost associated with curses limits their use. It is not something done lightly. Also, spirits may only be bound into a curse for a limited time before they dissipate, die or can break free, and demons or dark gods may eventually tire of the game. The stronger the curse, the longer the term may be.

A believable and versatile way to handle curses is make their establishment/enforcement dependent on the depth of attention the cursing person has earned with a supernatural entity, and their curse's relative alignment with the will of that entity.

For instance:

A pious, humble man is mugged in the night. As he watches the mugger flee with his money, anger, fear, and frustration well up and he utters a Curse, "God will see you receive the same!" In that moment, the man's God, whose very partial attention was drawn by the sudden, out-of-character utterance of His faithful, mirrors, just slightly, the same indignation at such an injustice. Part of Him hears the Curse and, since its intent resonates with His own, the tiniest sliver of His power manifests to carry it out.

Later that evening that same mugger cradles his own head in pain as another carries off the night's 'earnings'. In rage he utters a Curse, "God blight you eyes!". However, since this man's "God" was, publicly, the same one that carried out the Curse, the mugger was ignored and the curse had no power. Additionally, the God that the mugger really aligned with, a thieving and tricky fellow, found the whole thing hilarious and let the man wallow in his own self pity. Besides, why would he empower a Curse uttered against someone for doing what he would do?

Anyway, you get the idea. You can also add additional power/depth/plot around Curses with Faustian bargains and deific favors.

The tablet isn't the curse. It doesn't need to be.

Have you ever watched someone wrong you, and cursed them? Maybe someone blew through a red light, and you wished them ill. Most of the time you don't will them strong enough, but sometimes it happens. Sometimes the police officer is just 1 block away, and has already turned their lights on.

Sometimes that's karma. Other times you feel bad. A ticket is one thing, but a car accident is nothing to wish on someone over a mere red light. When they get in an accident, you start to feel guilty. Why? Because the curse worked.

Most of us can't curse coherently enough to do much more than that. It's difficult to hold a focus like that. If the average person tries, the curse gets diluted quickly... sometimes by someone else's curse. They may curse someone who drove through a puddle in front of them, and do so in a fuzzy enough way to accidentally curse your curse, weakening it.

Some people can make it work. Generally we try to run them out of town with pitchforks and torches.

As for the tablet? It's just there to help out using the power of language. Your true curse has no language, nor does it need one. You know exactly what you meant when you cursed. But if you're skilled enough at the cursing to curse along the lines of language, you may be able to make the curse more permanent. The language offers a scaffold of sort for the curse, helping maintain its meaning (over centuries if needed).

Likewise, a deity is just there to help out. They may lend extra firepower if your curse is true to their nature. They may lend it if you give a little bit of yourself to them. Depends on the deity. Just be careful with those curses. The deities obviously have their plan for the game, and sometimes the curse doesn't quite go as you mean it when you let a deity take over it for you. Better to pin it down with words instead.

As for balance, what if the curses don't exist? What if they're just a subjective illusion? What if that guy was going to get a ticket whether or not you willed it to happen? What if people really do just drop dead for no apparent reason? Uncertainty and doubt balance out curses rapidly. The more nuanced the curse, the harder it is to have developed a mind that leads the curse to come to pass.

And as for those minds that can curse, and curse well? Well the balance is even simpler there. It's as age old as time.

Be careful what you wish for.

The curse itself

Curses are spells, they need to be preformed very precisely. Things like cadence, intonation and word choice all affect the outcome. There could be even more requirements like the correct posture or cardinal direction of the speaker or something sillier like you have to circle your mouth with your tongue after speaking every O. Similar requirements (wording, kerning, the paper that's used) exist for written curses.

Everyday curses use the same or similar words, but they have no effect, because the other requirements are not met. They came about, because people saw actual curses having effect and were trying to replicate them.

Emotion

The curse would take effect only in the most extreme circumstances, based on how much hatred/desire/anger you could pour into the words when speaking them or writing them down. Most curses would only take hold when spoken by people who have been done a great injustice. Saying "I hope you trip" doesn't have nearly enough emotional power behind it to work.

Witches/warlocks could be people who have mastered controlling their emotions and can replicate that sort of emotional state on command.

The law

A bit of a different take, but curses are one-sided legal contracts in this world. When performed correctly, and after submitting the appropriate paperwork, the cursed is mandated to follow whatever requirements the curse put upon them or face much more horrible consequences handed out by the state.

Think of curses as as a stream of dark energy. In order for it to manifest, it has to solidify itself as a spell. However, the process of solidification is quite intricate. It depends on various factors such as intent of the person casting the curse, resistance of target, process involved in incribing the curse etc. Also, proper manifestation of spell requires a step by step ritual to be followed by the person casting the curse. Moreover, the curse intensifies if more people wish for that to happen.

When the person curses someone, a stream of negative energy releases from its body creating a void within him. Greater the curse, greater is the void created within. However, this void makes the spellcaster more susceptible to receive curses from other sources. Hence, the natural healing mechanism of the body kicks in, absorbing the curse back and filling the void. The rate at which the curse is absorbed depends upon the intent of spellcaster. More malicious the intent, greater the rate of spell solidification, lesser the rate of reabsorption.

So the daily curses like "I hate you Jim I hope you trip" seemingly have no effect as the spellcaster does not have malicious intent towards the target. Curses like these, spoken at the spur of the moment, are quickly absorbed negating it's effect. But curses written in stone or spoken a different way do have an effect as they are cast on purpose. Spellcaster has a malicious intent towards the victim and he wishes the curse to manifest and this accelerates solidification of curse into spell, thereby reducing its reabsorption. If the spellcaster's intent is strong enough, it also casts a rudimentary protection over the void created within to reduce its natural healing.

Yet, the intent itself is not enough for casting more complex curses. Normal folks with minimal spellcasting knowledge can make their curses effective with right intent, but it requires a real wizard/witch to cast highly devastating curses. Greater curses create greater voids thereby increasing the rate of curse reabsorption. A wizard/witch knows the exact ritual that seals the void created before the healing mechanism kicks in, thereby stabilizing the curse. The curses cast by specialists are more stable as they seal the void completely. As long as they can maintain the seal, the curse is effective. Greater the wizard/witch, greater the amount of void they can seal, greater the curses they can manifest. However, they have to be careful in estimating the amount of void they can hold. If they are not able to hold the void, the curse retaliates and brings their own destruction.

To overcome this problem, many witches and wizards work together to hold the void together. Many of them also exploit the intent of others to strengthen the curse. For example, for banning bishop Wulfric from building a cathedral over the ruins of the last one, the wizard exploits people's grudges against bishop Wulfric and their intent against building the cathedral and links them with the curse to strengthen it.

To carry out the curse of such magnitude specialists are required and someone would definitely ask for services of the wizard thereby making it valid. While a smaller level curse like forcing Otto to scream when he lies would be cast by a normal folk with hardly any malicious intent on a deeper level making it invalid.

I'd much rather leave a comment, but I don't have enough reputation to do so. I'd like to build on IAntoniazzi's answer:

If making sacrifices to a certain god or aligning to their cause makes them more likely to carry out your curse for you, then certain individuals with a long history of favouring certain gods will have an easier time convincing said gods to curse their target.

Some nobody might get a god to look their way if they perform a lengthy, rigorous and expensive ritual to place a curse on somebody, but an ancient, powerful witch who's served said god their whole life or at least carried out sacrifices and offerings often will be able to call on that god's help with a single word, being recognized instantly.

Geases are curses. Typically if someone breaks a geas they die. The main difference is that a geas usually has a condition attached to it like not being allowed to spill the blood of a boar.

You have to assume that magic is a real thing, like a great unseen extra dimensional ocean. Deities have vast access to this ocean, spirits less so, magic users even less. So average people trying to curse each other have little chance of doing so because they just can't tap into that magic source which turns will into reality. Even powerful magic users are limited to what they can achieve because the human mind can't imagine the processes required to will something more complex to happen - willing a tree to come into existence requires more than just wanting a tree to appear - you have to know how a tree is formed and grows to will it to do so. So most human magic is limited to creating elemental effects like wind and fire or cursing people to get sick and die or change their mind over some issue.

You could have groups of magic users coming together to perform more complex tasks where each user has focused on a specific piece of knowledge or even just to boost their connection to the source.

So it becomes more useful to try and get a spirit or god to fulfill your wish. That requires payment of some kind, the more powerful the being the higher the payment with some tasks only being performed by certain spirits who might not be the best creatures to deal with.
So perhaps you dedicate a temple or altar to a god or sacrifice the lives of animals or people - maybe giving up a valuable piece of jewelry or bags of money by depositing them in a temple or however else the being gets their reward.

How do they hear your curse? You could write it down and then deposit it in a spring or other site where magical beings come near the mortal world. If you can't write then you make a voodoo doll with the hair or clothing from your victim attached to it or chant a curse into the doll - imposing your will on the doll and then sending that off like a letter to Santa. Chanting an incantation while sacrificing a living creature or valuables is another way.

I'm making a fantasy world and wanted to incorporate curses and geases into the story. When I say "curses" I mean two types, but mainly this: Greek Curse Tablet

The type where you write your curse and either: perform a ritual, break it, or maybe bury it. But the classic "fairy tale" curses (the kind where a witch turns up and curses a prince) would also be a thing.

There is only 1 type of curse.
The kind that requires a ritual.

The problem is basically noone really understands the rituals.
They are far more complex than they seem.
What is needed varies by what the curse does.
And there are many rituals that can have the same effect.
Basically, can think of each ritual as a list of rules that need to be followed.

This is why sometimes random shouting can inadvertently cause a curse.
Because by chance the circumstances were right.

And why Curse Tablets sometimes fail.
The makers know say 9/10 of the components of the ritual.
What material, most of the actions, but they don't know the rest.

It is also why witches exist.
Turns out a common clause for many rituals is tied to the person making it.
If the 7th daughter of a 7th daughter, born on a full moon,
crosses her fingers and squints, then that is 95/100ths of the conditions for a multitude of different curses.

Curses are fueled by a soul fragment of the caster

Creating a curse is easy, you just have to put your soul in it, literally. Whenever you curse, a fragment of your soul splits off in order to form the curse. Maintaining the curse on the other hand, is difficult. The curse is still a fragment of your soul, and a soul desires to be whole. Therefore, the soul fragment and the original soul want to rejoin by their nature. With everyday curses, this happens instantaneous. Only with a lasting strong desire, be it born of righteousness or spite, the curse can endure over longer time. The curse does not require active maintenance, but it is still linked to your soul, so you need to believe in the cause of the curse. Once the belief wavers, the curse ends, but if it is strong enough, the soul rejoins the curse postmortem, which truly completes the curse.

So in the end, it is your own mind which decides which curses are valid as they are anchored by intent. You can make Otto scream when he lies, but only if you truly detest his lying ways from the depths of you heart. It doesn't matter if the curse is written or spoken, it's the thought that counts. Although following the proper ritual helps to transfer the soul in a state where it is easier to split a fragment. Witches are people who have a broken soul, which means that their soul fragments do not desire to rejoin the original soul. This allows them to curse on a whim, but those curses are easier to break as well.