I think your best option is to raise the flop to drive out gutshot straight draws and something like KJs from the big blind--the pot is big at this point and you need to maximize your chances of winning the hand. Assuming you get the BB to fold the preflop capper may either reraise or elect to slowplay KK or QQ (which is not a likely hand IMO) or figure he's behind or tied with AK. Since he capped preflop and is a tight player I think the only reasonable hands he could have are AA, KK or AK. Like it has already been said you are either way ahead or way behind at this point and the best hand at this point should win IN A HEADS-UP SITUATION. Assuming a call from the preflop capper and a check on the turn I think your best play is to check behind him and see what the river brings, even though it is largely irrelevent. You can assume a bet on the river with any of the above listed hands-which you just call. You have played your hand as cheaply as possible and he may even make a 'value' bet on the river with AK (which you win)-- this is all good. If you were to bet on the turn rather than checking it only bad things can happen (save the outside chance that he will fold AA). Either he will raise with a better hand or fold a worse hand. You will not have the chance of winning a river bet when he holds AK.

Assume a call on the flop and a bet on the turn when a blank hits. This presents a bit of a tough situation, but now I think you go into pay-off mode and call the turn and river-you can't risk being pushed out of this pot or showing that you can be pushed around after you have shown so much strength throughout the hand. I believe that if he did indeed have KK he would have gone for a check-raise on the turn rather than betting it out. So I would figure he has AK or AA-either of which is ok. If he has AK and bets again on the river that would be the ultimate-he's just giving his money to you. If he bets with AK and you raise it is doubtful that he will pay off a river bet and he probably won't even call your raise. But if he has AA who cares-not like it matters anyhow- a raise on the turn is too dangerous and alot of people fall in love with AA and won't fold regardless of the board. Let's say you do raise the turn here--what do you do when he three bets with KK--pay it off? Even though he is, IMO, more LIKELY to sandbag with KK on the turn maybe he's trying to win a REALLY big pot with his top set-hoping that you have QQ and will put in the max number of bets on the turn and river. Either way, that's a bad situation to be in, a raise in this situation is not an option.

Back to the raise on the flop. Assume it drives the BB out and the preflop capper reraises your raise. Now you're in a bit of a tough spot. You could call this reraise and see the turn--he will bet into you and your only play is to fold unless you improve (which is unlikely). Say you pick up a gutshot now--what do you do, call and chase to the river?? This is not a situation you want to be in. Assuming once more that this is a tight player, I think that if you are reraised on the flop you can safely fold your hand; figuring you must be against KK. If all he has is AK or AA then he HAS to be afraid that you flopped a set with KK or QQ and would be reluctant to cap the betting on the flop esp. with the strength you have represented.

So in short I think your correct play is to raise the flop and go from there. You can save some big bets if it gets reraised and win a small one and a big one if he calls and then bets the river. Or at least save a small bet by playing the hand for a raise on the flop.