That would depend on what the person was saying before they stopped talking and began staring. If I am talking to my husband, then stop and stare at him, it usually means I am really mad at him.
He might be interested in you. Usually there are more signs that the guy would do to show you that he likes you, but maybe he just doesn't feel the need to send you more signals.
stop and stare by one republic
OneRepublic
glare
You can listen to the One Republic's Stop and Stare for free on their YouTube channel. You will not only be able to listen but download as well.
omfg November 27 07 gosh I memorized that .... Stop and stare is an amazing song... ONE OF THE BEST SONG ONEREPUBLIC HAS.
to look intently; to stare angrily or with a scowl.
Pretending that they are staring at someone else.
you can say you glared or non stop looking
Stare at the bully awkwardly until he leaves you alone
Stop and Stare by One Republic
From Ancient Greek "homos," meaning similar, and Latin "stare," meaning "to remain."
He stops and stares, its like something taking over,