"Fat kids and dumb kids are also picked on. The natural tendency is to bully the weak and look up to the strong."
You are right, and it's deplorable. Schools do little or nothing about it -- that would be too judgmental, or worse, moral!
One of the favorite taunts of schoolyard bullies has always been, "gay!" I believe that this ganging-up behavior on kids is a prime source of the self-doubt that may lead to homosexuality. It probably has biological roots in the behavior of dominant males competing for females, and even dominant females competing for males, and it stinks.
Kids need to be loved and inoculated against this kind of baiting at school. Fathers and mothers who have effeminate sons or tomboy daughters need to constantly affirm to them that their interests and their gender are two different things, and that God made them their gender for a reason -- and to celebrate the opportunities it brings.
Some of it has to do with unsupervised play. The more it is organized, the more adults have control, the less bullying goes on. Left alone, kids tend to developed Hobbsean societies.