Late to the party but on the flop I would be calling as this is not a hand I'd be trying to generate fold equity with. You have a reasonable made hand with room to improve but want to keep villian's range wide - you are in bad shape with villains re-raise range of made flushes, sets and probably two-pair hands (though unlikely he has many of those in his range). He doesn't have many draws in his range (or made flushes to be fair) since you hold the As, so this raise doesn't seem like it will generate a ton of folds unless villain c-bets with air, even on such a wet board. The presence of a third player doesn't change much since you seem to have a read that he's weak - seems like they will fold whether you call or raise, but you also don't hate keeping this 3 ways with a call by V2, which may reduce the likelihood that you'll face a turn bet from V1 after 2 calls.
The villains call of the turn raise really narrows his range to overpairs and AK/AQ with a spade. With the turn brick, being OOP after raising puts you in a funny spot, another reason why a call on the flop may have been better. But I think the best play is check and evaluate the best plan based on villain bet size. He likely has an overpair and/or a high spade so he may check back and if not you should have a good sense of whether you have odds to call a bet from villain knowing you would likely need to improve. He is ahead here like 70% of the time (27 combos overpairs, 12 combos AK/AQo with a spade). I don't think you will fold out any of villain's range with a turn bet so don't see any reason to bet.
Obviously great card for you on the river, but if that was a blank I think I'd be checking expecting to see a check-back. Facing a bet, I would consider calling a small bet if I believed villain would bet small with a busted draw, but most likely folding. However, given the action and villain's range I would almost certainly expect a check-back unless he flopped a flush and played it very trappy to this point. This is also super unlikely given that you have the As and so there are only a few combos of flopped flushes he could even have had.