Aware: Middle English waren "to be mindful, be on guard," going back to Old English warian "to be wary, guard, protect," going back to Germanic warōjan- (whence Old Saxon waron "to attend to, protect," Old High German biwarōn, Old Norse vara "to warn," varask "to be on one's guard")

Awake: Old English wæccan to watch, Latin vegēre to enliven; Norwegian dialect vok, Old Norse vǫk hole in ice