Nl50 - Blindbattle with AQo

[Remoh007]

PokerStars No-Limit Hold'em, $0.50 BB (6 handed) Hand History Converter Tool from FlopTurnRiver.com (Format: 2+2 Forums)

Hero ($49.50)
BB ($79) unknown

Preflop: Hero is SB with Q[img]/images/graemlins/club.gif[/img], A[img]/images/graemlins/diamond.gif[/img].
<font color="#666666">4 folds</font>, <font color="#CC3333">Hero raises to $2</font>, BB calls $1.50.

Flop: ($4) 8[img]/images/graemlins/diamond.gif[/img], 6[img]/images/graemlins/spade.gif[/img], 7[img]/images/graemlins/heart.gif[/img] <font color="#0000FF">(2 players)</font>
<font color="#CC3333">Hero bets $2.5</font>, BB calls $2.50.

Turn: ($9) A[img]/images/graemlins/club.gif[/img] <font color="#0000FF">(2 players)</font>
<font color="#CC3333">Hero bets $5.5</font>, BB calls $5.50.

River: ($20) T[img]/images/graemlins/spade.gif[/img] <font color="#0000FF">(2 players)</font>
Hero checks, <font color="#CC3333">BB bets $35</font>, Hero folds.

Final Pot: $20

I'm very unsure about the best possible play in this hand.
I don't like it to make a continuation bet on this board but I do it with a bad feeling. Should I really check/call or even check/fold this flop?
And on the turn, I'm not sure how much I should bet.
And the river is another question [img]/images/graemlins/smile.gif[/img]
Is it too weak to check/fold it or should I bet something around 1/5 potsize as a blockbet?