[Man of Means]

Standard 3-bet against a button openraise. AQo obviously is as well. ATo could go either way since this is live - but against a somewhat aggressive player that recognizes position I'd 3 that also.

4-bet range is big aces, pocket pairs, maybe some big suited cards (KQs, ATs, KJs) and a slight chance of some weaker stuff. With a hand like 87s the 4-bet gives him fold equity when the board is something you might not like.

No clue on the flop check - a single pair would probably bet. This check tends to polarize his range to a flopped monster or a marginal drawing hand.

I'd call down to a turn 4-bet ... other than a flush, KJ is the nuts and you don't have that (although you do have a big re-draw if behind and I understand you want to exploit your "freeroll equity")