I personally bet the flop, it's not even like you were looking to checkraise.
Any king might make that play after you checking behind, KJ, a set...a lot of hands. I get all the money in personally, but I try and do it on the flop.
I also have zero talent at reading hands at this level, so I usually ride the variance.
I don't know, though. I assume you folded, if you're weak enough to check that flop. If you were checking it to induce betting, then by all means, bet.