An instruction to monitor someone or something, often because the person or thing in question may turn out to be dangerous. I think Tom's a thief, so keep your weather eye open around him. He needs to keep his weather eye open with this storm that's brewing, in case he has to evacuate.

An instruction to monitor someone or something, often because the person or thing in question may turn out to be dangerous. I think Tom's a thief, so keep a weather eye open around him. I'd keep a weather eye open with this storm that's brewing—we may have to evacuate.