While he may be checking behind JJ/QQ on this flop, those are the main hands you are ahead of here and want to get value from, and they have only 6 outs. You're very rarely going to be up against a huge draw. If any J or Q comes, you can be fairly confident your hand is dead, and I wouldn't be at all concerned about a diamond. These things allow you to play your hand pretty slow. I would c/c a flop bet and bet the river if the turn gets checked through, or if the flop checks through i would bet turn and shove river. If a J or Q pops up its just an instant check-fold. This line also is good because when you are behind AA or a set, sometimes a scary card will fall and villain shuts down after you call the flop and you avoid stacking yourself by bet/shoving or check/shoving the flop.