I think this is a really interesting discussion and interested in hearing others thoughts. I had a similar situation to this one. This hand happened, a long time ago, but the important parts are I raised to like 12 with AK in a 1/2 game, and got one caller in the bb. Flop is A66, he checks I check back the flop, turn he bets $50, so twice the pot. River he fires $100 and I think about it for a while and fold.
This was kind of a loose wild player who had been drinking. I thought about this hand a lot after the fact. Did he bet so big on the turn and river to make up for lost value with a huge hand? Or did my flop check make him think I was weak and so it induced a bluff from him that ultimately got through. When players do these 2-4x overbets on scary boards, are they doing it to make up for lost value with a monster, or are they just attacking weakness to take down the pot?