[drcapn]

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You have position on him correct? Why not just check behind him on the flop looking to get it in on the turn?

Villian is either way ahead and calling your flop bet or drawing to 2 outs with a smaller pp. The only way IMO you can get value from a worse hand is to check behind and see what he does on the turn. He could bet the turn with all hands he'd call the flop with along with lower pp's hoping to bluff you off of KK or QQ which he'd have to think is in your range at this point.

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I think this is clearly the best analysis so far. The bet on the flop won't fold hands better than you and might fold hands worse than you, who would otherwise take a shot on the turn.

Villian's range has not been discussed in detail, I'll start by stating the obvious:

(1) Cold calls 3bb PFR from early raiser
(2) Pot reraised, calls 540 into a pot of 1170 (~2.2:1)
(3) Checks the flop with Ace on board

He has 1750 left (29BB) and pot is 1710. He is comfortable enough to bluff at the pot on the turn.

So he really wanted to see a flop, but is not interested in taking a shot after the flop. AQs, AJs, ATs, maybe even KQs,QJs,JTs; middle to high pocket pairs. The aces aren't folding, but the others probably will, IMO, to the flop bet.
Thus I really don't see a reason to bet the flop.