This seems like kinda an obvious check behind. Since you wanted a list of pros & cons, I made one:
1) Our implied odds
suck. J/6 rivers rarely get us a ton of monies.
2) Villain calls 3-bets wide, so may have some Tx in his range he'll fold.
1) Villain folds to c-bets well, and called OOP. Likely has a strong range & isn't giving up.
2) We can still rep clubs on the river.
3) We always realize the equity our draw gives us (we don't have to bet/fold the turn when villain shoves).
4) Villain likely has started adjusting if you've been abusing him, and his likely adjustment will be to bluff catch more. Betting plays right into his strategy.