Re: bottom 2-pair on the turn
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If we're believing villain's story here and the K doesn't put out a flush draw I have a hard time putting him on a hand that doesn't have us beat here unless he would do this with just a Q or K. The question is then what hand does he b/c the flop with that contains no pair and a K? Nothing reasonable, I guess. I think KQ would have threeballed preflop and/or on the flop. The only logical hands that beat us are are K5, K6 and then there are the unlikely combos of 55, 66, KK or QQ (I'm discounting the big pairs very, very, VERY much). To me, that means the majority of the time villain's range has picked up outs here and is semi-bluffing us. That makes it an easy threebang. All of this is predicated on the turn putting out two of a suit.
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His play here is consistent with AK or AA. BB did three-ball pre-flop, but I have no idea why you think KQ might not just call the flop. I think that 66 and 55 are more reasonable hands for the villain to hold than K6 or K5.
I would be tempted to take the line of just calling down unless counterfeited or unless a five or a six falls on the river, in which case I would raise but maybe just call a three-bet.
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