IF your C-Bet percentage has been 100% i would continue to do so. When he folds it sucks that you hit the nuts and doesn't fit strong enough to continue. But the fact that you have C-Bet every time, should move some of the weaker made hands in his range into a call eventually.

I played a hand a year ago or so with a TAG regular (650) who i covered. He raised to 10 OTB, I called from the BB with 77. The flop came A75r. I checked intending to check raise. He C-bets a high% and has a lot of Ax hands in his button range. He checked back. The turn is a 6 and I bet 20, he flats. The River is a 4 i bet 40 and he flats, revealing AA. Had he bet or raised at any point he doubles through me.

Either he hs enough to continue or he doesn't. When you check to "let him catch up" you lose value from every "fit" hand in his range. If you're checking to let him hit a dead 2 outter, 92% of the time youll be dissappointed.