c.1300, "to go, glide, move," probably from O.N. sveigja
"to bend, swing, give way," from P.Gmc. *swaigijanan
and related to swag
(v.) and swing
. The sense of "swing, wave, waver" is first recorded c.1500. The noun meaning "controlling influence" (to be under the sway of
) is 1510, from a transitive sense of the verb in Du. and other languages. The verb in this sense is recorded in Eng. from 1593.