First off im a fish.

Second off my thought process here would be that on the flop we give up too much value by betting. This flop is extremely dry, and we have a very strong hand relative to our opponents betting ranges, but shorten the list of hands our villains continue with dramatically when we bet.

Both hand samples are very small, but the fish has been aggressive up to this point, and this is a flop alot of tags might be c betting. The only hands we really lose value from is a 56 type hand from fish. If the fish checks and the button c bets i dont like a check raise though because the board is so dry and villain may be folding a ton of his JT type hands. If villain is the type to give you his stack with alot of jacks here you will probably get it anyways, plus he can go berserk with dumb c bets or value town himself.

Ie. we are WA/WB the buttons c betting range and i would want to keep as much of the WA range as possible.