A 400bb+ pot size that I just played

Poker Stars, $0.25/$0.50 No Limit Hold'em Cash, 9 Players

BTN: $40.95 (81.9 bb)
SB: $60.14 (120.3 bb)
BB: $143.08 (286.2 bb)
UTG+1: $64.84 (129.7 bb)
UTG+2: $82.72 (165.4 bb)
MP1: $52.79 (105.6 bb)
Hero (MP2): $91.45 (182.9 bb)
MP3: $67.35 (134.7 bb)
CO: $145.80 (291.6 bb)

Preflop: Hero is MP2 with Q Q
3 folds, Hero raises to $1.50, 2 folds, BTN calls $1.50, SB folds, BB raises to $6.25, Hero calls $4.75, BTN calls $4.75

Flop: ($19) 5 Q 6 (3 players)
BB bets $9.25, Hero calls $9.25, BTN calls $9.25

Turn: ($46.75) 3 (3 players)
BB checks, Hero bets $25, BTN folds, BB raises to $127.58, Hero calls $50.95 and is all-in

River: ($198.65) 8 (2 players, 1 is all-in)

Results: $198.65 pot ($2.50 rake)
Final Board: 5 Q 6 3 8
BTN mucked and lost (-$15.50 net)
BB showed A A and won $0.00 (-$91.45 net)
Hero showed Q Q and won $196.15 ($104.70 net)

Preflop:

• BTN is a loose passive fish while BB is a regular. 
• Hence, I know that if I called BB 3 bet, BTN is most likely to call as well, making it a 3-way pot. A pair of Queens in this kind of multiway pot  is quite easy to play and I can get away from danger easily. Especially since the initial raiser is OOP. 
• Thus, I called. 

Flop:

• When BB cbets, I put him on a really strong hand, possibly AA-KK and possibly AK with a diamond flush draw. 
• Hence, I chose to call his cbet instead of reraising. I reasoned that if he has AA-KK, he will bet again. There is no need for me to reraise and chase everyone away when I have the nuts here. 
• Another reason why I chose to call is because both BB and I were both deep stacked. If BB has a flush draw, he still has 30% equity. I do not want to create such a huge variance by reraising BB which he is nv going to fold if he has the nut flush draw.
• Therefore, considering that there are more benefits to call BB cbet than to reraise him, I chose to underrepresent my hand and called his cbet. 
• I am not worried about BTN since he is playing such a wide range of hands and he is a fish!

Turn:

• I have the second nuts at turn now. 
• The only hand I lose to is 47. It is not likely that anyone is holding onto this hand, maybe with the exception of BTN, who is really capable of calling with any hand and since he is a mega calling station. 
• Perhaps, this is why BB checks. 
• Nevertheless,  I chose to lead out, betting half the pot, effectively putting BTN all in.
• However, BTN folds. 
• But BB shove all in!
• Not sure why he do this. But after analysing this hand, I came out with a couple of reasons:

1. His check at turn might be to pot control. 
2. He might think that BTN is capable of holding on to 47 hand and he might be beat. Putting money into the pot now serve no purpose. 
3. However, when BTN folds, he thinks that he might have the best hand. Especially since I under represented my hand. He will not be able to put me on sets+ since I didnt reraise his flop cbet. 
4. He couldn't put me on a set of 3 as well since he know I am a tag and would fold my pocket 3 at flop. 
5. Therefore, he shoved, hoping to get me off hands like flush draws.

• Considering all these factors, I think I have the nuts a large majority of the time and it is just so so unlikely that he has 47. Thus, I made an easy call. 

I think I played this hand quite well, ensuring that I get paid off handsomely and at the same time, reduced the variance which is inherent with deep stacked poker.