[Bianculli]

I agree that this is a worse two pair almost all of the time. If beat, I would expect to see a straight, not AK. If villain would bet a set 100% of the time on the turn, I don't see how he would play AK like this. He just calls with tptk why? To trap? Why trap with tptk if he is too scared to trap with a set? Or he played so slowly because he is worried about committing a lot of chips with one pair? Then why raise the river when there now are a whole host of hands that beat your unimproved one pair that you let get there cheaply?

I was not disagreeing with OP's read that villain would not check the set, but I just feel like this read also equally excludes AK.

I agree with a push as opposed to a smaller (but still large) raise. He most likely folds or calls to either rather than splits his decision.