QQ - Confused on turn

[Backstabr]

4/8 live

MP1 is not TAG, but is tighter and more aggressive than rest of the table.
MP2 is your standard LP calling station

Preflop: Hero is CO w/ QQ. MP1, MP2 limp. Hero raises, folded to BB who calls.

Flop comes Tc, 3h, 4h. Checked to hero who bets, BB folds, MP1 raises, MP2 calls, Hero 3-bets, MP1 caps, MP2 calls, Hero calls.

Turn is 2d. MP1 checks (!), MP2 checks, Hero ....?

I checked, but only because I was baffled. When MP1 capped, I was sure I faced two pair or better (34, 33, 44). How often am I missing a bet here by checking?