In a flitting manner; with quick, light, restless movements or in a way that doesn't stay in one place.
From 'flitting' (present participle of flitter) plus the -ly suffix that creates adverbs. Traces back through Old Norse 'flitra' but now describes how an action is performed rather than the action itself.
The -ly suffix is like English's way of saying 'in the style of'—so 'flittingly' means 'in the flitting style,' describing manner rather than meaning. It's how we transform verbs into descriptions of *how* something happens.
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