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1820, "tipsy, slightly drunk," from screw (n.) + -y (2.). Sense of "crazy, ridiculous" first recorded 1887. Related: Screwily; screwiness.
Very eccentric; crazy; nutty, screwball: Newspaper guys are mostly screwy
[1887+; fr the gait of a drunk person suggested by the twistiness of a screw thread, whence the various senses of deviation; influenced by the notion of having a screw loose in one's head]