[hatchfan]

I'd need to know more about the raiser and what the raiser thinks about the limper. If he'll raise a limper with AXs then maybe your play changes here, but against a typical player I fold. It can't be very +ev even if you all were to just check down, you don't close the action, and you're out of position for the whole hand.

You definitely don't want to commit yourself to the pot here if he's going to push, which even a 2000 chip raise will do. 1000 won't make him fold and since you're OOP it only marginally takes control of the hand. It does keep the pot smaller so you can continuation bet and still fold to a raise, but I don't find continuation bets out of position to work very often. Players love raising position on the flop and they'll think they can move you off of your hand due to the small but not desparate stack you'll have left. I hate being in spots where you technically could bet and still fold, but the only continuation bet that doesn't look weak is an allin (which still looks weak sometimes). Fold and wait for a better spot.
A call is reasonable, but ask yourself what you'll do if you hit an ace and he plays back at you. You need to know he plays bad aces aggressively when he hits and happily go to war, or know that when he pops you he has one of the good ones or two pair so you can fold. When I'm not sure about it I let AJo go here.

1)fold
2)call
---big gap---
3)all-in
4)1500-2000
5)1000