Because we will be OOP post flop, I'm not against flatting Villain's bet, because with a super short stack on the button this is and could look like a squeeze play to get V to fold and get HU with button. He then 4bets and we are in an ugly spot, OOP, playing for stacks if we call.
Assuming we flat from the SB, since we have no prior information about him because of lack of reraise pre, I'm alright with checking to the raiser here, not so much for V, but to maybe string along short stacked button. Villain bets out, Button goes all in would be ideal, but button folds.
Villain needs to realize that his bet on the flop, has a HUGE chance of being reraised by Button. That adds more strength to his bet, as I don't think he'd lead out to a pot with a short stack behind him without the intention of getting it all in. That means he has a piece of this flop (which we want) and we should let him continue his "lead".
With that being said, I'm okay with flatting again and seeing a turn. You're ahead with a straight and flush draw on board with no backdoor draws in your hand. His range has probably hit this flop or has some equity in the hand. KQ/AK/AQ/A10/Q10/K10 (hard to determine suites without knowing which cards on flop are club) type hands with two clubs or even one are staying in this hand and calling smallish raise. Check/call is fine. Raise just bloats pot and could make for very awkward turn and river cards/bets since you are OOP and have to check any club or card that completes a straight draw.
** Also ** You're post flop play has to do with your image and how you are perceived by the table. Are you a player that would raise light here? Would you raise a draw or are you only raising sets or two pairs?