Sorry for the full HH, but this is the best I can do with Microgaming because PT4 doesn't support it and I can't seem to edit it.

No reads.

Pre
Standard, maybe could raise a little bigger but I'm playing the hand OOP so I think it's ok

Flop

1) Is AK a good value hand to put into my checking range here? My thinking is that there aren't really any cards that I don't want to see, and the majority of V's calling range would be 2-pair combos

2) If I should bet, what part of villains range and I looking to get value from? Does he really have that much Qx, Jx here given the pre-flop action?

Turn
Pick up equity so I stab. No sure how this card affects the range he has here though. Any random Qx, Jx may call here given I checked the flop. Overall, I feel like my thought process isn't clear here because saying "I'm betting because I picked up equity" isn't a logical reason without an understanding of the ranges I'm working with

River
Just should have the best hand here so I bet. small trying to induce a curiosity call from any paint in his range. But honestly I have no idea what his range looks like at this point.

Overall, feel like I played this hand poorly. I'd love to hear how you are constructing V's range on this flop, the strongest hand you are putting into your check on this flop, and then any other thoughts about how I should be constructing ranges here. I was pretty lost from the flop onwards.