QQ in BB multiway action

Stars 2/4 6 handed game I get QQ in BB (I have ~ $575)
M/P (~$400) marginal player makes it $16 to go
L/P (~$650) cold calls $16
Q-n (I) What should I do? I called
Pot = $50

Flop comes out 7-3-3 rainbow

What should QQ do here? I checked, even though I think a better way to play it is to bet ~ $36

MP Bets $16
LP raises by $75 to $91 ...

Now it feels to me that MP missed, and LP is desperate to protect his 88-jj (hands that I think I can beat)

Pot = $157

What do you put these guys on?
What should I do with my QQ?