To labor hard or toil exhaustively.
From prefix 'be-' + 'swink' (from Old English 'swincan,' to toil). This archaic verb combined two intensifiers to mean 'to work oneself to exhaustion.'
Chaucer used 'swink' to describe hard labor, and 'beswink' made it even more intense — you weren't just working, you were beswinking yourself, completely exhausting yourself through labor.
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