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. People who are highly aggressive and dominating of others are more likely to control a majority of resources. 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.