I think that if you cbet the flop...you would have a better idea of what he had. If he only had midpair, he may have folded. If he called, he probably would have checked the turn.

Therefore, by cbetting, you may have him call (or reraise in which you would fold) and check the turn to see his action (little information is gained from us betting and him simply calling). A bet from him would be a fold. He may even check the turn (to keep the pot small) and give you a free card (damn, a jack would have been NICE in this situation). Remember that players love those KQ/KJ/QJ hands (though they really do suck) and will be calling them preflop (especially at the stakes we play).

The only reason I put him on A9 was because I was able to see the entire hand at once. There was no cbet so we are missing some information that we could have gained from doing so. The hand would have played out differently and I'm 100% sure that a player of your magnitude would have been able to put him on KQ (KJ being less likely since you have two).

And remember, you only have a pair of jacks. Here's a situation where we want to keep the pot as small as possible.