In a manner characteristic of a bully; in a way that involves intimidating or attacking those who are weaker.
From 'bullying' (present participle of 'bully' as a verb) plus the adverbial suffix '-ly' (Old English, from 'like'). The construction follows standard English patterns for turning adjectives and gerunds into adverbs.
English loves turning nearly any word into an adverb with '-ly,' but this creates something interesting: 'bullyingly' forces us to describe bullying behavior as a manner of action, which makes the aggression seem more calculated and deliberate than just 'bullying' does. It's grammatically subtle but psychologically revealing.
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