"I remember thine eyes well enough. Dost thou squiny at me?" So asks Shakespeare's mad King Lear of blind Gloucester, in an early use of the verb squinny in 1608. The word possibly comes from the earlier English squin-, the base of the Middle English of skwyn, meaning “on a slant.” The related and more familiar verb squint also appears in King Lear: "This is the foul fiend Flibbertigibbet.… He gives the web and the pin, / squints the eye, and makes the harelip; mildews the white wheat, / and hurts the poor creature of earth."
perhaps from squin- (base of Middle English of skwyn "on a slant," askoyn, ascoign "askance") + -y, reduced form of eye entry 1 — more at squint entry 1