NL10 QQ in 3bet pot

[Landogarner4]

Here's an interesting hand. MP just sat down, no reads. BB seems like a solid player, is multitabling, and has won money on all the tables I've seen him at. He is 24/14/1.35 over 77 hands.

I suspect I played this badly, tell me what you think.

Poker Stars - No Limit Hold'em Cash Game - $0.05/$0.10 Blinds - 6 Players - (LegoPoker Hand History Converter)

SB: $3.15
BB: $33.90
Hero (UTG): $10.30
MP: $5.00
CO: $7.35
BTN: $3.60

Preflop: Hero is dealt Q[img]/images/graemlins/spade.gif[/img] Q[img]/images/graemlins/heart.gif[/img] (6 Players)
<font color="red">Hero raises to $0.40</font>, <font color="red">MP raises to $1.50</font>, 3 folds, BB calls $1.40, Hero calls $1.10

I called here thinking I'd have easy play if overcards hit or if I flopped a set. MP doesn't have a lot of money behind but BB does.

Flop: ($4.55) 2[img]/images/graemlins/club.gif[/img] 9[img]/images/graemlins/heart.gif[/img] 5[img]/images/graemlins/club.gif[/img] (3 Players)
BB checks, Hero checks, <font color="red">MP bets all-in for $3.50</font>, BB calls $3.50, Hero calls $3.50

I knew MP was going to shove and I decided to call him. When BB flatcalled I started to hate my hand even more. I called anyway and I think this was a big mistake. I should have folded. Agree?

Turn: ($15.05) 5[img]/images/graemlins/diamond.gif[/img] (3 Players - 1 All-In)
BB checks, Hero checks

I think he wants me to bet. I want to see the river. I will save 53 BB if an A or K falls. I check.