Present participle of company; accompanying someone or keeping them company.
From company (from Old French compagnie) plus the present participle suffix -ing, meaning 'performing the action of being a company or companion'.
Companying is an archaic verb form you mostly see in older literature and poetry, but it reveals that 'company' used to be a verb meaning 'to be with someone'—languages constantly shift verbs into nouns and back.
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