There is another interpretation. To "eyeball" something or someone can mean to look intently at it or them, with a steady gaze. In this case, if you were eyeballing someone, they might not even be aware of it. In both Jura's and my definition, the stare is intensive and not considered polite. "The two guys seated at the bar eyeballed her as she walked by."

It means to look at someone squarely in the eyes to get their attention. or to scrutinize them. It is not considered polite to do this as by doing so you invade a person's personal space.