Wait... let's think about the bully for a minute. Where does bullying come from? My thinking is it comes from a few places, like seeing the family dynamics and figuring who is modeling the bullying behaviour. Shouldn't we also explore that if bullying behaviour is modeled at home, it would indicate that the bully lives in a very emotionally dysregulated home environment. Stressful. I'd be curious what other stressors are happening in the home, such as biological stressors (growing pains, hormone changes, medical issues, etc), maybe some emotional stressors (maybe being bullied by someone bigger than them, or watching it in the home, or having other emotional issues going on like not being able to identify how they are feeling), mental/cognitive stressors (too many expectations on them to perform, failing or falling behind in school, etc), social stressors (family dynamics, inability to make and keep friends, peer pressures), or prosocial stressors (inability to empathize, delayed character development, etc). Maybe bullying needs to be reframed as a dysregulated state that a person can't cope with, and taking it out on others is actually his or her way of saying "I need someone to co-regulate with me because I can't cope right now!"
And the one being bullied who goes and repeatedly seeks out help from the teacher is not just a wimpified kid who needs to grow a pair, but rather a dysregulated child who is also reaching out to an adult, and saying "a stressful social situation is happening and I don't know how to regulate. Will you co-regulate me so I am able to learn how to self-regulate in this situation?"
NO amount of bullying is justified, and all bullying behaviour needs to be reframed so the bully is not labeled as a bully, but rather is taught how to regulate him or herself in the face of stressors that they can't cope with. And a wimpy child is not a wimpy child, but needs to be reframed as a child who needs someone to co-regulate because they don't get enough co-regulation at home.
Anti-bullying campaigns and programs don't work. That's a proven fact. Teaching empathy is not working. So it's time to start looking at the reason why children really start using aggressive behaviours.