Etymology
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cockeyed (adj.)

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. Cockeye "a squinting eye" is attested from 1825.

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Definitions of cockeyed

cockeyed (adj.)
turned or twisted toward one side; "a...youth with a gorgeous red necktie all awry"- G.K.Chesterton;
Synonyms: askew / awry / lopsided / wonky / skew-whiff
cockeyed (adj.)
so unreasonable as to invite derision;
that's a cockeyed idea
cockeyed (adj.)
very drunk;
Synonyms: besotted / blind drunk / blotto / crocked / fuddled / loaded / pie-eyed / pissed / pixilated / plastered / slopped / sloshed / smashed / soaked / soused / sozzled / squiffy / stiff / tight / wet
From wordnet.princeton.edu