[Proofrock]

Perhaps I'm missing something in all of this discussion, but I think OP's point was that here he currently has a weak hand (one that he can't call a raise with), but he has a draw to a very strong hand. If he has either a strong hand or a weak hand, then CB isn't a problem because he has the easy decision if he gets played back at, but here he doesn't really want to fold, though he has to if Villain check-raises.

Whether to fire a CB here seems dependent upon Villain (does he play back frequently? is he aggressive, tricky, does he check-fold if he missed ...) and on Hero's image.

The possible outcomes, as I see them, are:
-check and take a free card.
-bet and take it down.
-bet and fold to a big raise.
-bet and shut down if called (unless you hit your draw).

Personally, I like checking in the given situation because we have a strong draw but a weak hand, we'll definitely get pushed off of our hand by a pair of kings or better on this board, and anybody without a pair of kings or better is unlikely to improve on the turn. So if it gets checked to us again, we have the option of betting the turn, and with a greater likelihood that our bet will take the pot. If Villain leads the turn, we can let pot odds/implied odds make our decision for us. Besides, checking the flop adds some deception to your play -- not only do you demonstrate that you won't CB 100% of the time, but if you've been active and people suspect you of CBing without a hand, a thinking Villain may also expect you to CB when connect with the flop (flush draw here).

The argument that checking invites Villain to take the hand away on the turn I find a little lacking. The same player who bluffs the turn with a weak hand is just as / more capable of check-raising the flop.