c.1300, "to go, glide, move," probably from Old Norse sveigja "to bend, swing, give way," from Proto-Germanic *swaigijanan and related to swag (v.) and swing. The sense of "swing, wave, waver" is first recorded c.1500. Related: Swayed; swaying. The noun meaning "controlling influence" (to be under the sway of) is 1510s, from a transitive sense of the verb in Dutch and other languages. The verb in this sense is recorded in English from 1590s.