i think that capping the flop is a mistake vs. this guy. he has defined his hand as a big pair, and it's likely AA. the problem is that you can't fold on that board, so just call the 3bet and get to SD cheaply.
the turn is the dumbest card ever. you probably can fold now as the only hand you beat is JJ or a really stupidly played AK.
in a live 3/6 game vs said player i can probably fold here on that card though that could be effected by what you think he thinks of you. you said that you have been running the table over with your hot cards. perhaps he has been patiently waiting for a hand to beat you with so he could be overplaying a hand vs you here, though given the action there doesn't seem to be that many hands he can have here that makes too much sense that you beat.
He knows I play solid. I had been running over the table but I wasn't playing out of line by any means. Just running insanely good and not missing a flop. I ended up calling down out of frustration and a little confusion more than anything and he showed AA. Given a couple more seconds to think it through I probably should have let it go. Just can't beat most of his range.