QQ and a fish: c/f this flop?

Very soft table. UTG+1 is an unknown, but a tight player so far. This is the first hand they played after 1 orbit. Button is a wonderful little fish, calls down with anything, hardly ever raises preflop, and never raises after the flop. Stats on him are 57/1.4/.4, with flop AF .21 and turn AF .3.

PokerStars 0.25/0.50 Hold'em (10 handed) FTR converter on zerodivide.cx

Preflop: Hero is UTG+2 with Q[img]/images/graemlins/diamond.gif[/img], Q[img]/images/graemlins/heart.gif[/img].
<font color="#666666">1 fold</font>, <font color="#CC3333">UTG+1 raises</font>, <font color="#CC3333">Hero 3-bets</font>, <font color="#666666">4 folds</font>, fish calls, <font color="#666666">2 folds</font>, UTG+1 calls.

Flop: (10.40 SB) A[img]/images/graemlins/club.gif[/img], 4[img]/images/graemlins/spade.gif[/img], 7[img]/images/graemlins/heart.gif[/img] <font color="#0000FF">(3 players)</font>
UTG+1 checks, <font color="#CC3333">Hero bets</font>, fish calls, UTG+1 calls.

UTG+1 is not a big concern yet, but the fish is... I'm thinking A-rag here, but he could be on a 7 and just calling down like all good fish do.

Turn: (6.70 BB) 7[img]/images/graemlins/spade.gif[/img] <font color="#0000FF">(3 players)</font>
UTG+1 checks, Hero checks, <font color="#CC3333">fish bets</font>, UTG+1 folds, Hero folds.

I check here to see what the fish does. With a turn AF of .3, I don't see him leading out with anything less than an A or the trip-7's. He bets, I just don't see what he could have that I beat, so I lay it down.

So all this got me thinking. When playing against a fish like this, is it better to just check/fold the flop when an A comes against your big pair? Or would that qualify for a skirt? [img]/images/graemlins/smile.gif[/img] I mean, with an AF of .3, a guy like this is only gonna bet if he has a big hand right? And he did cold-call a 3-bet. What fish cold-calls a 3-bet unless he has an A or a K? I'm trying to figure out if I played this flop correctly or not...