By bullying, I mean individuals harassing others with name-calling or violence but not for the purpose of gaining resources such as with extortion or theft. The only explanation I've thought of is that bullying offers practice for types of extortion that do result in increased resources.
I think bullying is really more of an emergent behavior that manifests itself because of natural aggression built in for survival, as well as our complex social-based psychology leading to insecurity when dealing with other:
People who are highly aggressive, and or apathetic to the suffering of others are more likely to control a majority of resources if they don't face significant opposition. This leads to their favored propagation obviously. Then, in their free-time, with all resources under control, they simply continue to do what comes naturally to them: dominating others. It can also work even in those without the ability to actually control resources, due to lack of intelligence for instance. I have met far more non-intelligent bullies than the reverse. The reason for their behavior is still explained by an attempt to control their territory and social status, however ineffective.
Again, due to our complex psychology centered around social interaction, we can develop insecurities about our self-perceived 'fitness', and therefore acceptance by mates and peers. This low self-esteem can lead to bullying others to boost one's ego. Chemically, this can result in a release of endorphins because they feel they have achieved something, which supports bullying behavior as an emergent behavior. Also, those with lower intelligence are likely to have trouble with reasoning skills, and therefore find it difficult to self-analyze and realize their behavior is negative. This leads to bad interactions with others, which can make those individuals feel even more insecure, which in turn fuels their drive to assert themselves through bullying.
Many studies have been conducted on sociopaths/psychopaths. Just like any other evolved trait, whether or not their "personality disorder" is beneficial to the propagation of their genes depends on environmental factors. If they face only opposition from entities that are relatively weak, physically and mentally, then they have an advantage over those peers. But if their peers are sufficiently strong and organized, then the personality disorder becomes a disadvantage if they can't adapt, because they will be attacked by those seeking cooperation from others when they misbehave. Obviously, when our species' numbers were few, high-aggression and a willingness to kill for resources needed for survival aided in survival. In these modern times, its less acceptable for socio/psychopaths to display their innate behavior, due to modern laws, but obviously society can take turns that allow them to express themselves without worry...see the holocaust or any other genocide for an example.