Try to stack him or control pot? 5/10 6max

[diconoclastx]

Maybe this is a boring hand. I have AQs. One limps. I raise on the button. Blinds fold. It is headsup. Villain is tight preflop, not sure postflop.

About 100 in pot now. Flop comes AA9. He checks. I bet pot. He calls. I'm certain he doesn't have AK or 99 because he would have raised those preflop.

Turn [Pot: 300ish]. offsuit 4. He checks. I check.

River [Pot: 300ish]. Another offsuit rag. He bets 250ish. I call.

Standard? Who bets the turn hard in an attempt to stack an inferior ace here?