Is Tuesday named for a one-handed god?
late 14c., an astrological term, "streaming ethereal power from the stars acting upon character or destiny of men," from Old French influence "emanation from the stars that acts upon one's character and destiny" (13c.), also "a flow of water," from Medieval Latin influentia "a flowing in" (also used in the astrological sense), from Latin influentem (nominative influens), present participle of influere "to flow into," from in- "into, in, on, upon" (see in- (2)) + fluere "to flow" (see fluent). Meaning "exercise of personal power by human beings" is from mid-15c.; meaning "exertion of unseen influence by persons" is from 1580s (a sense already in Medieval Latin, e.g. Aquinas). Under the influence "drunk" first attested 1866.
1650s, from influence (n.). Related: Influenced; influencing.