What weight has the kamma when forced to do bad things as a child? Example: A child (+/- 8yrs old) is forced to kill an animal. It doesn't want to, but has to because it is threatened by abusive adults.

Wanting to kill or not doesn't, I think, matter when it comes to the bad kamma performed here. And yes, since it is the child that performs the killing, the bad kamma is done by the child and the child will bear the negative results of that kamma.

But, what about the weight of that kamma? Since the child had no option but to obey. How heavy is that kamma? How heavy can the results be?
Does anyone have an idea (preferably with source to text in the Pali canon)?

(Related: What is the Buddhist perspective on child abuse? . Except that that question was about the cause, mine is about the weight of kamma.)
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.