Without a read, I don't think folding is a huge leak, but I would lead toward calling down. If he had 76, you just counterfeited him.

A turn K would make me lean toward folding, since we have to dodge 6 cards in the deck that could be in his hand instead of just 2.

I'd play K6 more conservatively, since villain can hold a few more overcards that could hit on the river. But not many more.