I usually play it like Roy said.

I do this especially because he raises too much preflop. If you lead, he'll fold AT-AK type hands, where if you check, he might check behind and get a free one.

Also, if you are going to check raise, and you are willing to be all in, I say just CR all in. It smacks them around a bit more.

Honestly, I don't like showing AI with just a straight draw, if you are called here you are well behind an overpair and coinflipping with a flush draw like A9s. I think that most overpairs are going to call here putting hero on a draw with this AI. Secondly if I played this way I prefer that villian is tight rather than loose, so that I have some folding equity.

I thought a bit about how I would play it if I don't just fold on flop.
If I had some read that villian is not going to fire 2 barrels with just overcards I would just call his CB, figuring that I can be ahead (and it wll be easy to find out on turn) , if not I have some outs, and even if he has an overpair there is so many scare cards, that he is unlikely to lead turn and I could draw to my straight.

All-in-all I think it is an interesting situation on flop that deserves some more discussion.