Villain is 29.3/13.1/2.37/988 hands

I'm thinking the only thing that I did right on this hand was pre-flop. Should I have just pushed this flop after his raise?

Full Tilt Poker
No Limit Holdem Ring game
Blinds: $0.50/$1
6 players
Converter

Pre-flop: (6 players) Hero is CO with K A
2 folds, Hero raises to $3.5, Button calls, 2 folds.

Flop: A 9 4 ($8.5, 2 players)
Hero bets $6, Button raises to $15, Hero calls.

Turn: T ($38.5, 2 players)
Hero checks, Button bets $22, Hero calls.

River: 5 ($82.5, 2 players)
Hero checks, Button is all-in $57.3, Hero calls.

Results:
Final pot: $197.1

Not pretty mate, he can only have AdXd, hope you didn't go broke with 1 pair

I think I'm almost always check/shoving the turn after the board gets really drawy. If he has a set at that point, I'm just going to lose because the board is too heavy.

On the river, I don't think I would call his shove without a good read. Ugh, brutal hand.