AK vs river raise

this is fine

Nice hand.

Well played.

I would play the same way.

Pre-flop completely standard.

The flop is very dry. The ace hits your UTG range very hard, so a cbet here is the standard move. You should considering checking sometimes against a good opponent so that you don't become so easily read.
But overall cbetting is fine. The size you used is good too.
Now, when he calls what hands does he do it with? Knowing you opened from UTG and an ace appears, he has to have something as well.
I think suited broadway hands are folding. AX is very possible. A set /two-pair are also calling instead of raising here to keep your potencial bluffs. High pocket pairs are unlikely given the PF action.

The turn is blank imo. Betting again is the standard play. Nothing wrong with it.
But when he calls here I think we are behind. A weak ace is probably folding to our bet.
AT+ are continuing.
This call looks like a slowplay from a monster to me.

But now the river comes a 3. So it makes it unlikely the set of 3's. 4's don't make sense as well because of the flop.
His range here is something like: AT+, A7's, A3's, A4's, 77.
When you are in spot like this facing a decision between getting value by betting or by checking, you have to ask yourself: "What hands would they bet if I check?". If does hands are the exact same ones as the ones they would call your bet, then you bet.

In this spot, if you check he's definitely betting hands that you lose to. AT+ is probably checking-behind to see if they're good.

There are almost no hands that he's calling with and you beat. Only the AT+ hands.
Unless this is a really bold move and he's bluffing, you're beaten most of the times.
Lets review the hand:
- PF call IP;
- Flop call IP;
- Turn call IP;
- River shoves to a 3rd barrel from an OOP player/UTG raise, on a ace high board.
This is clearly a value shove.

That said, I'm check-calling here if he goes really small, check-folding if he goes bigger.

I play the same, guy seems to be legit he just calls AJ AQ and shove 77 33, there is to small chance that hes bluffing this river, so im totaly fine with bet folding, check is losing value, check call makes no sence because only better hands will bet this river maybe sometimes AQ but not always.