What's missing here is what this guy's image of you is. Does he think you are a straightforward player betting your hand? Have you pulled off or attempted a few bluffs? semi-bluffs? If he puts you on a flush draw, he could really have a large range of hands. If he thinks you are betting top pair, then I think he has two pair or a set of 6s.

It's hard to say really. I'm folding here if I have a tight table image because I would believe his strength. If I've been consistently raising flush draws and suspect that's what he has put me on, it may be a different story.

With no raise before the flop, both players should be wary of the range of hands we could both have. Your raise on the flop bet is the only information. It's a tough spot.