I do prefer betting out but was going with Rhound's play in suggesting the check-raise. I think it depends largely on what kind of plays you've been making, and I don't have a real problem with throwing in a different way of playing the hand occasionally. But I don't see the function of check-calling unless you're trying to rep 97 or 75.

As to the check-fold, there are VERY few players against whom I would suggest that, but there are indeed one or two. From the description, I was thinking this is likely one.

The thing is, KK with position after the A is only getting called by a superior hand. Ok, on a board of 866, the check-call on the flop MIGHT look like 97. But 97 is also clearly going to lay down if KK bets. I really think JJ-KK are going to be happy to just check it down as a general rule. I suppose JJ MIGHT get some fold equity out of QQ, but after the original limp, it would seem very strange for Rhound to have that hand. Moreover, this really isn't the kind of player who's thinking about how to fold superior hands but more worried that he's beat if he has JJ-KK.

Basically, after the flop action, JJ-KK are gaining absolutely nothing by betting--except the intangible equity of not showing, but the price on that is just way too big in this pot imo. Rhound can't call with 99 or TT but will generally call with any 6 or 88, and that's really about it.