AQo misses the flop

[scotty34]

I have button as a mouse, but that's only been 21 hands. He has called twice and raised once over those 21. This read may not be worth much.
MP1 is a typical fish. Will call with almost any 2 preflop and will bet pairs, but is quite passive once raised.

Party Poker 1/2 Hold'em (10 handed) converter

Preflop: Hero is MP2 with Q[img]/images/graemlins/spade.gif[/img], A[img]/images/graemlins/diamond.gif[/img].
<font color="#666666">1 fold</font>, UTG+1 calls, <font color="#666666">1 fold</font>, MP1 calls, <font color="#CC3333">Hero raises</font>, <font color="#666666">2 folds</font>, <font color="#CC3333">Button 3-bets</font>, SB calls, <font color="#666666">1 fold</font>, UTG+1 calls, MP1 calls, Hero calls.

Flop: (16 SB) 6[img]/images/graemlins/club.gif[/img], 5[img]/images/graemlins/diamond.gif[/img], T[img]/images/graemlins/spade.gif[/img] <font color="#0000FF">(5 players)</font>
SB checks, UTG+1 checks, <font color="#CC3333">MP1 bets</font>, Hero calls, <font color="#CC3333">Button raises</font>, SB folds, UTG+1 folds, MP1 calls, Hero calls.

Turn: (11 BB) Q[img]/images/graemlins/heart.gif[/img] <font color="#0000FF">(3 players)</font>
MP1 checks, Hero checks, <font color="#CC3333">Button bets</font>, MP1 calls, Hero calls.

River: (14 BB) 8[img]/images/graemlins/diamond.gif[/img] <font color="#0000FF">(3 players)</font>
MP1 checks, Hero checks, <font color="#CC3333">Button bets</font>, MP1 folds, Hero calls.

Final Pot: 16 BB

I know my flop play is VERY questionable, and looking back at it, I really do not like it. I would have folded to an MP1 3-bet. I planned to check-fold the turn UI. I think folding the flop would have been the better play. Thoughts?
Once that Q hits, what do you think of the check-call line? Again, I'm not so sure about it. If I had a more solid read on Button it would have been easier. Is this one of those way ahead/way behind situations that is warranting of check-call?