You have a big hand. You want to build a big pot. Checking the flop makes it very hard to do that.
It also looks mighty strange if you 3bet preflop and then don't follow through with a cBet on the flop here. How actively have you been 3betting? What does he perceive your 3bet range to be?
What do you think his 3bet calling range is OOP? Most likely something that's hit this board, so punish him with your nuts.
If his calling range is only low/mid pocket pairs and he's only observed you 3betting a very narrow range, a check will probably induce action from lesser hands on the turn, especially if he puts you on a scared AK or 99/TT.
But overall, I'd say cbetting is the way to go here. Your hand is well hidden and you want to get as much money in the middle as possible.