OP, I understand your logic for checking ace high boards in 3bet pots... I do the same thing to balance my range against good players.
But in this particular situation I would not take this line because of the unique dynamic at this table - since both V1's opening range and V2's flatting range are very weak, I'm going to be 3betting a whole lot more hands for value in this spot - hands like KQs/KJs/QJs which are going to want to bluff on ace high boards. Given this wider range, I should have a good balance of value/bluffs on these boards, I no longer want to be checking everything with all of the extra hands I can have, especially oop.
On this particular flop, I get that his continuing range is going to be very small when you cbet. But as others have eluded to, you're not going to induce a whole lot more action from him by checking... all of the hands he's folding to a cbet are also going to check back and fold to a turn bet unless he turns a set (pretty hard to do), a straight (really bad for us), or he has exactly K
J off and turns a spade (a hand that's pretty likely to fold preflop imo). Maybe checking is ok if he has a lot of weak aces in his range but that seems very unlikely to me.
As played, once you check the flop you can't raise his bet. You have to protect your range as intended. And now you're in a really annoying spot on the turn in which you probably just have to begrudgingly check/call again. Check/raising has some merit if you don't think he has many flushes in his range. Leading is terrible for the same reason c/r the flop is terrible. And btw he literally never has AA ever... idk why some people itt think he does.