There's only so much you can do to avoid looking strong. At some point you have to put money into the pot and hope your opponents have hands good enough to pay you off. Checking and then cold calling a raise is going to look pretty damn strong anyway, plus it gives your opponents a chance to play perfectly on the next street.

If you haven't already, you should watch my Getting Paid series. It's possible that betting the flop is actually better than checking, even with an aggressive player on the button. Betting is more consistent with how you would play a variety of hands weaker than a set, whereas checking and then putting money into the pot after someone else bets is something you're more likely to do with only strong hands. Then again, you got your opponents to put quite a lot of money into the pot before “tipping your hand”, so to speak, so even if you didn't get stacks in you did win a good bit as a result of your check. The result you got here is definitely not a bad one.

takedown said:

I prefer on multiway pots with drawing boards that you lead. People float with all sorts of crap these days and if you take a lead, check turn line a lot more chips can go in the pot. Your bet will just look like a standard cbet and all sorts of good things can happen.

I agree with this, but I'll add that it depends how often you'd actually c-bet air in this spot. In a spot that you'd frequently check-fold (multiway pot, board that hits people's ranges hard), check-raising strong-but-vulnerable hands is good. When you're going to bet your air, then betting your strong hands is good.