Betting the flop does not get all worse hands to fold... almost all pairs will peel.
By checking you telegraph the strengh of your hand to your opponent.
IMO checking back here is waving a flag saying you are now ready to get barelled off whatever it is you're holding there.

I'd c-bet half pot. Fold to a raise, unless you have reads that he will c/r bluff Axx boards with air.

It's also betting for protection... and you can all beat me off... betting for protection is legit, yo.
If he want's to bluff you off he has to either c/r this flop which represents a really narrow range. Or he has to c/c, donk turn - which isn't in the playbook of most microstakes players. or c/c c/r turn... all that on a board where he can't really have any draws.
But if you check back he can just mash pot on two streets and he doesn't risk nearly as much.

I check back there against some regs, but against the same regs I will check back AK, sets and some backdoor draws, and raise the turn a bunch. But that's not a great idea against unnkowns.