also eye-ball, 1580s, from eye (n.) + ball (n.1). As a verb, 1901, American English slang. Related: Eyeballed; eyeballing.
eyeball eye·ball (ī'bôl')n.
The globe-shaped portion of the eye surrounded by the socket and covered externally by the eyelids. Also called bulb of eye.
The eye itself.
To look at; look over; scope on •An isolated instance is attested in 1901: He would eyeball the idol-breaker/ You locate trophies before they eyeball you (1940s+ Black)
give someone the fish-eye, up to one's eyeballs