10/20 limit, quick turn issue HU

I think you bet and give him a chance to fold. He might have been willing to call a small bet on the flop with K-K-Q-J but not a big bet on the turn. Or if he's pulling for low, he might not be willing to throw down a big bet heads up for 1/2 the pot. The turn card couldn't possibly have helped him. The only way he seems to have you is if he's got a 7, but I am guessing he would have bet out if he hit and try to get you, who he might think has a low hand, to fold. I know I would bet there and not risk giving you a chance at a free card to make a low, if I had a high hand.