To be appropriate or acceptable for someone; to suit or fit well.
From prefix 'be-' + 'suit' (from Old French 'sivre,' to follow). This archaic form means the same as 'suit' but with the intensive prefix that was common in Middle English.
You'll find 'besuit' in Shakespeare and the Bible, but it's completely vanished from modern English — we kept 'suit' but dropped the 'be-' version, showing how prefixes can be dropped when the base word alone does the job.
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