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1580s, variant of Middle English slike (see slick (adj.)). Originally of healthy-looking animal hair; applied to persons 1630s, with sense of "plump and smooth-skinned." Figurative meaning "slick, fawning, flattering" is from 1590s.
"make sleek," mid-15c., a variant of slick (v.). Related: Sleeked; sleeking.