Why can’t Tom stand to look at Amy?

Tom couldn't bear to look at Amy because he'd broken her heart.

A good part of the whispering had been occasioned by an event which was more or less rare--the entrance of visitors: lawyer Thatcher, accompanied by a very feeble and aged man; a fine, portly, middle-aged gentleman with iron-gray hair; and a dignified lady who was doubtless the latter's wife. The lady was leading a child. Tom had been restless and full of chafings and repinings; conscience-smitten, too--he could not meet Amy Lawrence's eye, he could not brook her loving gaze.