hi,
in 4bet pots, you only need to cbet 33-40% of the pot on dry flops. No point betting any larger. You are putting the same amount of pressure on his entire range. The pot is already big so even a 33% pot size bet = 29 cents (14.5BB) and that's a lot of money.
Checking Flop is probably the better option and while future streets might be hard to play, it certainly seems better than turning your hand into a bluff where no worse hands call and no better hands fold.