1. To look over a person so as to evaluate and form an opinion of their appearance and demeanor. I could feel everyone eyeing me up as I made my way toward the main stage.

2. To look attentively upon or at someone in whom one is romantically or sexually interested. There's a really cute guy eyeing you up from across the bar.

1. To look at someone carefully in order to make a judgment about them. I saw the other poker players eyeing me up, trying to figure out if I was any good.

2. To look at someone or something in a way that indicates desire, attraction, or sexual interest. You're totally eyeing up that cute blonde over there, aren't you? I've been eyeing up the dessert menu, but everything looks so good. I can't decide what to order.