You check/raise all-in with stacks this deep? That's real bad, IMO.

And my thinking was if I check/raise pot-sized and get called (possibly by KK/AA with a heart), I have to commit another big bet on the river if I don't catch anything to try to make him lay his hand down. And by c/r or betting the turn, I lose any money I would make if this is a bluff. I also assumed with overs/JJ-AA he would check behind, because it's such a scary board and I could get to a cheap showdown.

But you're right, I had absolutely no plan and ended up just calling down, which can't at all be good. But stacks are way too deep, IMO, to be f'ng around here either.