What weight has the kamma when forced to do bad things as a child?

Buddha has said "intention is kamma". The action done without any intention to do so is not binding. Here the child is not having any kind of intention ,so with this as the base ,action done by him is not burdened upon him. It is burdened upon the person making to do so. The intention is governed by the sankharas . If at all physical action does not happen but still anyone has intention to do so is binding. The intention itself is governed by the greed,hate etc. If intention is there and you do not do physical action . For not doing physical action there might be several reasons. Not getting proper situation, mind controlling it by saying no this is not good etc . But the arisal of intention can only be dispensed with when observing it equanimously. Not by controlling it through mind. It only suppresses it for the time being, again to crop up on receipt of stimulating inputs from sensory bases. There are n number of intentions (seeds of kamma) stored . So one is always under misconception that though bad intention aroused ,i have not done any physical action upon it ,i have controlled myself. But this misconception does not relieve from the burden of the same. Buddha has said there are kaya kamma,vacha kamma and mental kamma. Behind all of these are the volitions/sankharas, which are generated by us only out of the avijja/ignorance of anicca,anatta. Sometimes our actions/response are so involuntary that after happening of that action we come to know of it. Here again there comes into play the reacting habit/conditioning of the mind ,strongly in that particular type of sankharas. The conscious even does not know it. But as the buddha said all arising is to pass away,it is not permanent. But this happens in our case only when the wisdom of anicca develops within us at experiential level. But once it develops, no bothering of arising of whatsoever. In hinduism there is a nice nomenclature about this .that stage is called upon as 'avdhoot/paramhansa". Then there is no bothering of rules/regulations of scriptures etc bcs whatever action happens is not causing any burden to repay.

Karma is something very complected to fully comprehend and Buddha advice not to attempt comprehending it as a result.

Remember that Karma is intentional action.

In this example the child does build up Karma for killing. But did he enjoy or be happy about it. Will this lead to further killing by him compared to someone who killed on his/her own free will. All this are part of the equations. There is a difference in reluctantly killing, which can be done even by a stream entered person.

People who forced him/her to kill will also build up karma from it. And they are more likely to repeat the pattern and build up more karma as a result compared to child.

Also the karma of the animal that was killed also played a part in it. But non of it is an excuse.

Also child might regret his action and live in guilt. Which is also bad karma. In Theravada buddhism at least, I have heard a story about a monk who became a snake after death as a result of indulging in guilt of breaking off a leaf of a tree (This original action of breaking a leaf was not even intentional nor bad karma but the guilt was).

One important thing to take here is that it is incorrect to say the child had no choice and he had to obay. This is incorrect. Every human being is free and can choose to disobey if they want. Such action may have consequences, so is killing.

This thinking of we had no choice, is a result of years of conditioning our minds to be obedient, conformatives instead of being free.

I don't think it possible for sentient beings to objectively quantify the weight of karma. In other words, there is no objective answer to this question that will properly quantify the weight of negative karma relative to other acts.

What is clear is that negative karma will almost certainly accrue. How do we know this? Because being forced to kill is unsatisfactory. It is disturbing to the mind. It will leave a negative imprint.

Now, is it possible that some child is actually an advanced Bodhisattva or Buddha manifesting as a child and what appears to us mundane sentient beings as a child being forced to do harm could in actuality be an enlightened being manifesting and doing acts that are ultimately beneficial motivated by compassion? Yes! This is possible. In such a case, no negative karma will accrue for that manifesting being. That being's mind will not be disturbed even the slightest bit.

However, if the child is an ordinary sentient being then the predicament is negative and the fruits of it are going to be at least in part negative. Why do I say at least in part? Maybe the child also has a thought of compassion for whatever sentient being it is forced to kill. That compassionate thought is virtuous and will without a doubt manifest positive fruit. Nevertheless, negative thoughts most certainly will also arise and give negative fruit.

Anyway, I don't think we can quantify it. I think we can say it is most likely some negative stuff going on and children forced to do this type of thing are going to be negatively impacted both in the moment when they are forced into a negative act and in the future as negative fruit ripens.

One thing to keep in mind is that karma is not justice. It is not like there is some court or bank that is keeping tally of our good/bad deeds and doling out consequences accordingly. It is not like that. Karma and the law of karma just are the way things work. Children don't deserve this kind of thing happening to them. On the other hand, they don't not deserve it either. Deserve / not deserve, does not apply. Karma just is.