I really don't see any value at all in raising the river as played here. For sure AA is the only hand that calls you, I suppose KK finds a call sometimes, QQ even less. You can run into 99, KJ, AJ. I mean, we think from his preflop raise size he has a big hand but people play strange.
I am trying to get a handle on how many chips you have left on the river. He bets 4,300 but how much does he have behind? If you raise then you can't fold if he shoves, just in case he is some kind of maniac who thinks AA is the nuts always and it won't be much more.
I like a turn check because I'm not really comfortable at all with getting it in here in the main event. In some more turboish tourney, with a lower buy in then sure, but in the main event, I'd be sick if I got all my chips in with this hand. So I like the check for that reason and also to bluffcatch.
Flop: I am 55/45 in favour of a check. My decision would likely be based on factors such as live reads and experience with this opponent.
But when you do bet, as played, I am 100% in favour of the turn check and just calling the river.