There's a lot of hands he could have.

At this point you're getting 5:1 from the pot. You have no draw, and two overcards. Whatever he has, it's probably better than ace high. I would look at it as if he has a pair of nines or an overpair in the hole (tens or jacks), and play it accordingly, discounting implied odds entirely - because even if you catch an ace or king you don't know for sure you are ahead, and you don't know if you can get much more money out of him. This is a grey area but I probably fold just based on the pot odds, which are slightly unfavorable even if all six of your outs are clean.

Option 2 is to proceed as if you have an overpair and keep firing away. I hate doing this without a read on my opponent, and I hate doing it out of position. On this hand I don't think I'd bother.