What are you looking at me for meaning?

An aggressive and threatening rhetorical question used when one feels that another person has been staring in an inappropriate way.

What to respond to what are you looking at?

If you were staring at them, intentionally or otherwise, you could say “sorry or “nothing” and just turn away. It is likely the person will appreciate feeling like they have their privacy back and not feeling stared at… or through. You can also choose to tell them what was on your mind as you stared.