Have your eye on somebody Definition 1 of 3Pro Tip 1/3Suspicion Used when someone's behavior raises doubts or concerns. The cashier had her eye on the shopper who kept looking around nervously. Pro Tip 2/3Observation Suggests ongoing, careful watching of someone's actions. The teacher had his eye on students during the test to prevent cheating. Pro Tip 3/3Vigilance Implies being alert or ready for possible problems. Parents always have their eye on the kids at the playground.