In large amounts or with great abundance; done excessively or generously.
From Latin 'profusus' (poured forth), from 'profundere' (pro- + fundere, to pour). The adverbial form developed in Middle English from the adjective 'profuse.'
When something happens 'profusely,' it literally means it's been 'poured out' in abundance—that's why you sweat profusely when nervous, because sweat is literally pouring from your body!
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