AA facing turn push

[Proofrock]

Here are my thoughts on the hand.

The turn bet looked strange to me. I would expect a set/2 pair to 3bet all-in on the flop, or check-raise all-in on the turn. The king didn't make any likely two pair, KK would probably have reraised preflop. Check-minraise seems like a strange way to play a draw, but maybe he planned to minbet the turn if he missed ... at any rate, the most likely hands I figured him for were 7cxc or Kdxd.

Results in white below:
<font color="white"> Villain showed K K and I didn't improve. </font>