Preflop and flop seem standard to me, I don’t think I’m ever folding or raising either street. I don’t like folding to future bets as a general rule, but if villain has been barreling relentlessly then I guess you could make an argument for a very tight fold on the flop, because there are very few run-outs that K7 is happy calling down on.

I think you are correct that the turn check-raise was a mistake. It’s understandable to want to protect your pair against all the possible draws, but I don’t think villain has as many draws as you might imagine. To have a flush draw villain needs to have an off-suit preflop hand, and a huge chunk of villain’s off-suit cutoff range has a pair on this flop. Similarly, a lot of gut-shots will also have a pair on this board. Even very aggro villains are likely to check back a hand like JT on either the flop or turn, with or without the J.

I think it’s often wrong to fold second pair to a turn barrel when the top card pairs, but boards with 3 Broadway cards are harder to miss and harder to bluff. I strongly prefer folding turn but, if you are continuing, I think calling with a plan to call most rivers is best. This keeps villain’s range as wide as possible, and you will definitely catch some bluffs. Check-raising for protection means you are forcing weak draws to fold some equity, but also denying yourself what may be a profitable river bluff-catch opportunity. The range that calls your check-raise has you crushed.