I know an elderly woman who's been an avid golfer all her life. She has a pre-zinc penny in her golf bag that she uses as a golf ball marker. Her golf ball marker penny is ground down on one side only (obverse), exactly how the OP's penny is, with the high point at the very center. Perhaps this is why the OP's penny is also ground down. Someone used it as a golf ball marker.
To me it looks like a pair of lips that may have a selfish and stupid meaning. Hope I'm wrong. Stupid is what stupid does!