How to maximize this hand?

[iceman5]

Some bankground first.

$2/$4NL.
Here are my last 2 hands prior to the one in question.
I raise to $24 with QQ. I get a caller.
The flop is KT4. I bet 3/4 pot and get called.
The turn is a queen. I check hoping to check raise big but he checks behind.
River is an ace. I check and call a small bet. He has KJ and wins with a straight.
We have a "discussion" when he starts trying to taunt me.

Couple hands later. 6 limpers and I raise to $32 from the SB with JJ. Same guy reraises to $60. We both have pretty big stacks so I call. The flop is Jxx. I check raise him all in and bust his AA.


OK, because of these hands ( my raise to $32 with JJ), I have a feeling people dont respect my raises. On to the hand in question.
I open raise UTG to $20 with QQ. UTG +1 calls (different guy now),MP calls and then the BB min raises to $36. We all call.

Of course I think hes got AA or KK most likely. UTG+1 is very loose but Ive never seen MP or the BB before. They all have about $400 and I have them covered.

The pot is $146 and the flop comes KQ4. The question is does he have AA or KK? The BB leads out for $24. That doesnt look like AA. It looks alot like KK to me.

I just call. UTG+1 calls also. MP folds.

The pot is $218. The turn is the case queen. The BB bets only $20 now.

How do you maximize this hand from this point on? If I raise, it'll look like I have AQ. I'll lose UTG+1 for sure, but of course if the BB has KK, I'll bust him. If he has AA or AK, he folds also most likely.

I know this isnt the most thought provoking hand, I just wonder whats the best way to maximize profits since theres another guy behind me still in the hand.

It looks like theyre both scared since the BB is betting smaller each round and the UTG+1 isnt raising, so I may not get much more no matter what I do.