There are internal and external norms and even norms within each category have different levels of importance.
External norms are typically of the nature of "no fighting" and are enforced without looking at the circumstances. Their goal is for somebody perceived as an authority to keep the group pacified and minimize visible conflict. They are typically not interested in invisible conflict because by its nature, the external power can't see it.
The goal is not justice, it's peace.
Internal norms are fuzzy because they're usually not codified and might not even be agreed upon by the members of the group because their goal is maintaining a social hierarchy within the group.
The hierarchy's goal is neither peace nor justice, it doesn't even have a goal, it's just a compromise between people with differing goals - some entirely uninterested in the hierarchy, some obsessed with climbing the social ladder.
However, every group/organization is just a collection of its members who each have different incentives. For some of those, it's gaining status/power. Status/power is mostly a zero-sum game, therefore gaining it requires attacking others (causing conflict). But causing visible conflict is damaging to the group so other members are likely to punish such behavior. As a result, the optimal strategy is to cause conduct conflict invisibly.
Bullying is nothing more than such a parasitic individual trying to achieve status/power or in some cases simply satisfaction.