Yes a turn check in hindsight looks best, not sure what we're hoping that calls the turn bet that we beat and it's not uncommon for regs to bet flop and check-shove turns in 3bet pots like this. Such a common line at the lower stakes.

I'm pretty tempted to call the river when the K pairs given they know have less value and and the odds we're getting are pretty good so we don't have to be right that often.

I think Harvie covers this really.

I think you're lucky you didn't get shipped on and have a profitable call withyour draw.It's a disaster if you don't realise all the equity you have here.

I think I like your river fold once he's raised the turn.I just don't see him playing AT or worse this way unless it's an airball bluff