[chief444]

I'm thinking CO's most likely holdings here are a worse A or other overcard combinations such as KT-KQ, JT, QT, QJ, or even K8, Q8, etc depending on how much he attempts to steal. It seems likely that any pair would raise the flop with button still in. So you're probably way ahead here most of the time, way behind a smaller percentage of the time, and he may be drawing to more outs than I'm thinking a smaller percentage of the time. But it's not a very draw heavy board.

However, I still like a check/raise because he'll bet a worse ace and call down. Bet/3-bet is another option if he'll raise any Ace but I don't think he would, or at least he wouldn't always.

The other thing is, even if he is behind without an ace he will still bet the turn sometimes.

If you think he would just call the flop with T9-K9 or other possible pair +5 out combinations though then it seems betting becomes a better option because he's probably loose enough to call down to a bet but may check through the turn or may fold to a check/raise if he does bet. Basically, if he plays a little loose and fairly aggressive postflop I think check/raising is better. If he plays more than a little loose and passive postflop then I think betting is better. If he plays well postflop then I like to check/raise a decent amount on the turn anyway.