AQ unimproved HU OOP - how far to go?

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I played this hand couple of days ago, but it keeps bugging me so I'd like to hear some critique.
Standard players at these stakes are loose-passive, but I haven't sat on the table enough to note anything specific about anyone.


PokerStars $0.10/$0.20 Limit Hold'em - 6 players
Hand Converter Tool from DeucesCracked.com

Preflop: Hero is BB with Q[img]/images/graemlins/heart.gif[/img], A[img]/images/graemlins/spade.gif[/img]
UTG folds, MP calls, CO folds, Button calls, SB folds, <font color="#FF0000">Hero raises</font>, MP calls, Button calls.

Flop: (6.50 SB) 2[img]/images/graemlins/spade.gif[/img], 4[img]/images/graemlins/heart.gif[/img], 4[img]/images/graemlins/diamond.gif[/img] <font color="#0000FF">(3 players)</font>
<font color="#FF0000">Hero bets</font>, MP folds, <font color="#FF0000">Button raises</font>, Hero calls.

No question here about calling his raise. But in LPP games should one tend to give credit here to some made hand instead of raising based on the very dry board? Should I make at this point decision to lean towards folding once I dont improve?

Turn: (5.25 BB) T[img]/images/graemlins/diamond.gif[/img] <font color="#0000FF">(2 players)</font>
Hero checks, <font color="#FF0000">Button bets</font>, Hero calls.

How to proceed here? Should I fold unimproved already here? If calling, is it with the intention to call most rivers also? If calling, is it with the intention to fold most rivers since LPP is unlikely to bluff 3 barrels?

River: (7.25 BB) K[img]/images/graemlins/spade.gif[/img] <font color="#0000FF">(2 players)</font>
Hero checks, <font color="#FF0000">Button bets</font>, Hero calls.

Turn+river cards are definately in his range in case he held overs on the flop. Getting 8-to-1 is this a call with some showdown value to make a note against unknown or fold?

Final Pot: 9.25 BB


Several mistakes here I believe and several spots where different players proceed differently. I'd love to hear your thoughts.