Eye-contact represents honesty in the U.S. He's trying to tell you he's being sincere.
The funny thing is that eye-contact is considered disrespectful in Japan and China. That's why we need to understand everything about cultural gestures and their meanings, before we go there. My professor told me that when he taught in Bulgaria, he noticed that it's the only country where people nod to say "no"/disagree and shake their head to say "yes"/agree. :)