Your line is not good.

What was the point with the turn bet? If he raised the flop with a worse hand like TT-99 he will probably not check behind on the turn. AQ might, but that hand is very unlikely.

And with his better and the splitting hand, he may raise, and there is no point of throwing your 2 outer away for no reason. And sometimes he's bluffing.

Its better to not chase away his worse hands. Let him bet the turn. And probably c/c a blank river too IMO. b/c would be spewing and b/f is not good either because he will probably not pay off with the lower pairs. c/f is the alternative, but I prefer a call.