[mjkidd]

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AK and AQ have 6 outs to beat you and are getting 8-1 on a call, so they would be correct to call.

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Good argument. If it's 3-betted on the turn: cap, call down, or fold?

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There's no way you can fold this hand to a turn 3bet. Sure, AT might have just caught up, but he could have a slowplayed A4 just as easily. He might have a set, but he could just as likely be overplaying a hand like A9-AK. I call down to a turn 3-bet, but I think capping isn't terrible. It puts you in a bad spot if you get check-raised on the river, though.

I guess James' line minimizes the amount lost in this spot (you'll get 3-bet with AT or a set on the the turn) while keeping the amount won when ahead the same. The BB likely won't 3-bet AT on the river, and he might even just call with a set of fours.

Will you fold to a river 3-bet? I would call against an unknown.