The worst bullies I saw where from well off families. Still weren't the brightest, but that had definitely nothing to do with social circumstances. In fact, those socially handicapped kids were those being bullied. That was on a German Gymnasium, so on the road to higher education.

Obviously, social dynamics will be different in lower tier schools. I do have the impression that we are not discussing those here.

Also, being bullied is a poor excuse of becoming a bully yourself.