The flop cbet doesn't really accomplish too much. If he folds he had a hand with very little equity. If he calls you put in money with less than 50% equity, so you lose some of the money you put in.
I much prefer to check flop and then call a turn bet on most cards. You will still put in money against all better hands, you but can pick up some bluffs that way.
The turn cbet is the same thing really. Why are you betting? Seems very random to me. He won't fold a Jack, so bluffing makes no sense. He will call 98 
:club: and similar hands but it's not a value bet either.
Maybe your plan is to triple barrel starting on the flop, thinking that he will fold a lot of hands on the river? I think that is good plan, but I don't like it with A9, I would like that more if you have had a draw or a hand with substantially less showdown value. Like T8 or Q3.
When he raises turn he represents QT and possibly 99/K2s/K9s for value. I don't expect him to play this line for thin value with a hand like KT, though it might be a good idea for him to do that if you are habitually 2barreling hands like this. As bluffs he represents AT for sure, and then a lot of 'maybe'-hands like AQ,Axcc,9xcc,Q8s,TT,97ss.
It's difficult to know what his frequencies are here on the turn. How often would he play QT like that instead of raising flop? How often would he float flop with Q8s and then bluff raise turn?
Personally I don't expect him to bluff here too much, so I would fold rather strong hands like AK. But since you like barreling so much given you barreled A9, maybe he will be bluffing here a good amount of the time.
In any case, A9 is too weak to continue against a turn raise, so just fold.
