Hello there quant1986, thank you for sharing your hand with us. Very good hand!
Without further duo, I will say right off the bat that I really don't love flating AQs from the BTN. Specially versus UTG.
If the player in the CO raises and I see there is one or two recreational players at the blinds, than I would THINK before calling, because I don't think AQs will play very well, even in position versus unkown ranges. If the player doesn't fold very much too 3-bet it is a 3-bet 100% of times, for value. Yes.
If the player in the UTG is opening wildly such as 18%, 20%, 25%, maybe your call it is okay. You gotta have information of what SB and BB are going to do after you flat.
IMO, we will get preflop 4 combos of AQs. As a personal rule of thumb, I will be 3betting 3 combos and calling 1, at maximum.
Then, the Big Blind player Squeezes versus UTG and BTN. Okay, we gotta stop here a second and take a breath: how does AQs will play postflop in a Squeezed pot? What if UTG calls? Can we call? If UTG calls, and we call and we miss the flop completely or comes a Tx, Jx, Kx, how can we play our hand?
I believe BB doesn't have too many bluffs in its range when it decides to Squeeze versus UTG. BB doesn't know if UTG is going to call or 4-bet and BB doesn't know about the Button either. Do you see many wild players Squeezing out of position versus UTG for bluff, when, for odds, it is much better for the BB to call with a medium-strong hand because of the odds? Squeezing from the BB remove the odds the BB had preflop for calling and now put the BB in a very dangerous spot. I don't see many bluffs here.
Perhaps if the BB was Squeezing versus CO and BTN, I could maybe agree with your call here.
What if we UTG folds, and we call and we hit TP2K, are we happy if Villain Big Blind makes a bet bigger than 1/3 pot? Are we ready to stack off right here, in the name of the lord?

You don't have enough volume of hands for taking any definitive conclusion about Villain.
One thing the population of CardsChat will agree (I hope) with me: micro-stakes players are dumb-dull-jerks when it comes to fold equity. They are not folding Ace high sometimes, if they believe you are bluffing.
These stats you gave are not enough for a bluff river. We should know how often % this particular player 3bet/Squeeze out of position, and we must have at least 1000 hands for taking any conclusion about 3-bet or Squeezes.
When you bet river Villain has all the combos of JJ, AJ, AA, KK and QQ, and you in the Button will have NONE of these combos, because you would never played like this, except, maybe if you in the BTN had AJs.
When you bet the river you are trying to represent a decent hand, which you don't have: If you really had AA, KK or even AKs would you be flatting versus a Squeezor from the Big Blind which you consider "spewy"? Would you be checking turn for "pot control" and sending a bullet in the river?
Does this spewy player knows what do you know? And if the spewy player knows, can it exploit you to the bones? Yes, she/he can, and she/he will!
It's a non-sense line: you called 1/3 pot flop, and AJ would never be doing it, because AJ could be raising right here for value and protection.:icon_clow
Pocket JJ also would never be calling 1/3 pot in the flop, unless you had one Jack of clubs, even so it would be much better to be raising this if you don't have a blocker of clubs, because your set also needs protection. You can never have the blocker of clubs because the jack of clubs is in the flop, which reduces a little your combinations. So...
Perhaps, you want to represent low pairs that could be cold calling versus UTG raisor and then Cold Calling Squeeze: wild players elect to call Squeezes or even mini-4bet pots with pocket pairs such as 66 and 55, so don't try to represent those, you wouldn't have too much and if you had I believe you would be raising for the same reasons AJ (with the ace of clubs maybe), and JJ could and should be raising this 1/3 pot bet in the flop.
AQ suited without any backdoors, without any pair, it is a very easy fold. AQs is very weak in a board like this, we have nothing but bluffs, we have double bluffs, because we called a raisor from UTG and called Squeeze.
If you really believed the BB player was a maniac you should be 4-betting AQs FOR VALUE, for pure value, in the case, of course the BB maniac is 3-betting/Squeezing too much.
Nonetheless, I believe your prior mistake was to cold call versus UTG. AQs is very dominated by UTG's range and will not have a good playability postflop. So if we decide to 3-bet AQs versus UTG, we can represent and have initiative in a lot of board where AQs in position will destroy playing a 4-bet pot.
When you 4-bet there is a really small chance of some crazy nitty to told AK, AJ, AT, 77 and under, etc at the micros is hard, but it is a nice pot if UTG folds, rake free, let's consider a lot of facts before taking wild lines because we have "AQs, AKs, AA, etc".
We are not playing hands: we are playing our adversaries in the first place.
Regards;
Carlos 'Aballinamion' Barbosa