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1821, "squint-eyed," perhaps from cock (v.) in some sense + eye (n.). Figurative sense of "absurd, askew, crazy" is from 1896; that of "drunk" is attested from 1926.
Askew; crooked; Slonchways: He put his hat on cockeyed and got a polite chuckle (1910s+)
i'll tell the world