Wow, this one is nasty, but ill take the plunge. As bb was closing the action, there are a lot of possibilities, depending on the player (a more detailed read would certainly help). One thing I don't really fear here is AA or KK, as I think most "solid aggressive" players would reraise these preflop with this action. I'm not sure how accurate this is with your read, but that is how I would interpret it.

A set may be wanting to protect their hand here. If villain likes closing the action with various semi-garbage hands because he thinks he has implied odds on you due to your image and due to all the people already in, hands like A2s, 5/4s, 6/5s etc become possible, albeit very unlikely (I hope, or he isn't as solid as you may think [img]/images/graemlins/tongue.gif[/img]). Just about any pocket pair can be betting like this as well, and QQ is ahead of that kind of range here, especially since I don't really fear AA or KK given my interpretation of hero's read. Therefor, this is going to be a WA/WB situation the majority of the time (he would have to have something like 66 for it to not be). I really don't like raising here, therefor I make the call. If MP2/SB don't wake up with a hand, I have position throughout the hand on BB, and I expect a check on most turns a decent % of the time. I think it gets tricky if SB or MP2 come along for the ride. If either one repops, I go away.

I think I likely call down BB if it does get HU and he continues firing. Let him put his money in with his overpair. I check behind if he checks turn. I value bet river if he checks both streets. No real point to raising him at any point, and I am ahead of his range. I wish I had a better read than what you gave me though, as this may change some of my thoughts.