AQ with trip Q's on the flop vs. loose aggressive villain

[l0uway]

Villain stats are 70/40/4
What should I have done differently here? I thought he was holding AK, so I was trying to extract more money on the turn and river. He ended up having AT.

Absolute Poker No-Limit Hold'em, $0.10 BB (4 handed) Hand History converter Courtesy of PokerZion.com

Button ($20.50)
SB ($3.90)
BB ($41.80)
Hero ($13.55)

Preflop: Hero is UTG with A[[img]/images/graemlins/diamond.gif[/img]], Q[[img]/images/graemlins/spade.gif[/img]].
[color=Red]Hero raises to $0.4</font>, [color=Gray]1 fold</font>, SB calls $0.35, [color=Red]BB raises to $1.2</font>, Hero calls $0.80, SB calls $0.80.

Flop: ($3.60) K[[img]/images/graemlins/spade.gif[/img]], Q[[img]/images/graemlins/club.gif[/img]], Q[[img]/images/graemlins/heart.gif[/img]] [color=Blue](3 players)</font>
SB checks, [color=Red]BB bets $1.1</font>, [color=Red]Hero raises to $4</font>, SB folds, BB calls $2.90.

Turn: ($11.60) 5[[img]/images/graemlins/diamond.gif[/img]] [color=Blue](2 players)</font>
BB checks, [color=Red]Hero bets $3</font>, BB calls $3.

River: ($17.60) J[[img]/images/graemlins/heart.gif[/img]] [color=Blue](2 players)</font>
BB checks, Hero calls $5.35 (All-In), BB calls $5.35.

Final Pot: $28.30