The most likely suspects are always the people who had acces to time alone with Burke. The "usual suspects" in no particular order would be; teachers, coaches, clergy, anyone who worked in the home regularly, immediate family, extended family, family friends.
In this case, ultimately either his father, or an extended family member would be my guess. It's possible JAR did it to him also, but in that case, someone would have done it to JAR or unless JaR had age innapropriate issues in that regard, but to my knowledge we have heard no such thing. If JAR did know that Butke was ill and/or bring molestated....his forgiveness statement would make a lot of sense. Perhaps he understood what drove Burke more then anyone.
I wonder if when Burke started acting out, they would punish him, and keep JBR closet. Dotting on her, giving her more attention, all in an attempt to make up for the abuse she suffered at the hands of her brother. Much like parents often over compensate to keep their children happy during a divorce.
The problem was Burke was likely acting out for attention in large part. He saw the attention once focused only on him, get taken away and directed at JBR. He acts out, because he lacks strong expressive language skills. But when he does it back fires, and JBR just gets more attention....he doesn't get why, and gets more frustrated, and he still can't expressive so he acts out. I think the animosity was building for a while, and I think the parents efforts to "comfort" JBR after such incidents may have added to his increased rage.
In his head he might have truly thought he could just get rid of her, and it would all get back to normal.