In a drunken manner; in the way or fashion of a drunk person; intoxicatedly.
From 'drunken' + '-wise' (manner or direction suffix from Old English 'wīse'), creating an adverbial form meaning 'in drunken fashion,' common in Middle and Early Modern English.
The '-wise' suffix is one of the oldest ways to make adverbs in English—you can still see it in 'likewise' and 'clockwise,' but 'drunkenwise' reminds us it once meant 'in that particular manner,' not just 'in that direction'!
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