Wiktionary
keep a weather eye open
vb. (context intransitive idiomatic English) to maintain a background awareness of something; to remain alert to changes without it occupying your full attention.
Usage examples of "keep a weather eye open".
The special responsibility, of course, is to keep a weather eye open for Sovbloc illegals and couriers-and so forth.
The special responsibility, of course, is to keep a weather eye open for Sovbloc illegals and couriers—.
I tipped him the wink and as he knew you were due he thought I'd better stay on shore to keep a weather eye open.
He or she would want to be awake, to plan the next atrocity and keep a weather eye open for pursuers.