AJ as overcards+gutshot vs check/raise from LAG. How to play?

[Akimka]

BB is LAG. VPIP 28, PFR 18, postflop 3.67/1.8/1.0
65 hands on him

How would you play this against him?

Party Poker 2/4 Hold'em (9 handed) converter (http://www.selachian.com/tools/bisonconverter/hhconverter.cgi)

Preflop: Hero is MP1 with A/images/graemlins/diamond.gif, J/images/graemlins/club.gif. CO posts a blind of $2.
<font color="#666666">2 folds</font>, <font color="#CC3333">Hero raises</font>, <font color="#666666">5 folds</font>, BB calls.

Flop: (5.50 SB) 9/images/graemlins/heart.gif, 7/images/graemlins/spade.gif, T/images/graemlins/diamond.gif <font color="#0000FF">(2 players)</font>
BB checks, <font color="#CC3333">Hero bets</font>, <font color="#CC3333">BB raises</font>, Hero calls.

Turn: (4.75 BB) A/images/graemlins/club.gif <font color="#0000FF">(2 players)</font>
<font color="#CC3333">BB bets</font>, <font color="#CC3333">Hero raises</font>, <font color="#CC3333">BB 3-bets</font>, Hero calls.

River: (10.75 BB) 7/images/graemlins/diamond.gif <font color="#0000FF">(2 players)</font>
<font color="#CC3333">BB bets</font>, Hero calls.

Final Pot: 12.75 BB

[spydog]

I will often smooth-call the turn and raise any non-threatening river. You are less likely to be 3-bet on the river if you are behind, so you might save yourself a bet. Plus, raising the turn might make him throw away a worse hand, costing you 1-2BB.

If I'm not afraid of a flop cap, I would 3-bet the flop and take a free turn card unimproved. However, judging by your opponent he is likely to cap, so I like the call.

[PokerBob]

Looks fine to me.