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I'd bet, but not that big. The most I'd bet would probably be about half the size of the pot, but more likely what I bet preflop (5xBB).
A check looks like a monster after preflop betting big like that. A good player wouldn't fall for that trap unless they also had a monster, in which case they'll play along with you even if you bet.
An all in doesn't look like a 9, and certainly not quads, true. But it looks like an overpair, and a good tight player would fold AJ and probably even QQ here. If a good player played a hand like that with that flop I'd certainly put him on KK or QQ. With QQ, a good tight player should be reasonably sure you have at least KK, and not be happy about it, but be able to lay it down. With KK they'll probably call since it looks like QQ, as they probably wouldn't think you'd play AA, JJ, or any 9 like that. But they're only likely to call with JJ, AA, and KK, and no matter how you play it you'll get all of JJ's chips and probably AA's. The all in option would probably only be best if you have a loose aggressive image.
With the standard bet at the flop, they really gain no new information about your hand, particularly if you often bluff at a pot in the same fashion. With this bet you really could have any hand that you would've made a 5xBB preflop bet with, whether that be AK, AQ, QQ, TT, AJ, etc.
And the big bonus is now you're inviting a hand like AJ or QQ to reraise you rather big, as they have no reason to believe that their hand isn't good. Checking may get them to bet once or so, but they'll be much more likely to fold to any raise by you, possibly completely stop betting after you check call on the flop, and be extremely unlikely to play back at you on any street, as they should be smelling a serious monster being slowplayed (i.e. JJ) if you check call on the flop after a big preflop raise.
The way I'd play the hand would be entirely different if I called someone else's raise, as I'd slow play then for sure, but if you make a big preflop raise from early position they'll expect you to bet again at a flop like this with almost anything you have, unless you're an extremely passive player.
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