Green’s Dictionary of Slang

(US/W.I.) an unpleasant look, a disapproving stare.

1953		R. Chandler Long Good-Bye 177: I went back close to the bed and stood looking down at him, giving him the hard eye.
1974		G.V. Higgins Cogan’s Trade (1975) 86: Look, the last time I come in, you’re giving me the hardeyes, I look like a bum.
2019		S.M. Jones Lives Laid Away [ebook] One fat ICE bastard hard-eyeing me had a splotch of guacamole on his vest.