"move back and forth," Old English wafian "to wave with the hands" (related to wæfre "wavering, restless"), from Germanic *wab- (Old Norse vafra "to hover about," Germanic waben "to wave, undulate"), from PIE root *webh- "to move to and fro, to weave" Meaning "to make a sign by a wave of the hand" is from 1510s.
Heat wave is from 1843
To make waves "cause trouble" is attested from 1962.