$5 NLHE 6-max: Bad call?

PokerStars - $0.05 NL (6 max) - Holdem - 5 players
Hand converted by PokerTracker 4

BB: 100 BB (VPIP: 28.95, PFR: 23.68, 3Bet Preflop: 0.00, hands: 41)
UTG: 41.4 BB (VPIP: 32.32, PFR: 23.17, 3Bet Preflop: 7.56, Hands: 337)
CO: 136.6 BB (VPIP: 21.54, PFR: 12.31, 3Bet Preflop: 3.13, Hands: 65)
Hero (BTN): 100 BB
SB: 128.4 BB (VPIP: 21.79, PFR: 14.10, 3Bet Preflop: 3.85, Hands: 80)

SB posts SB 0.4 BB, BB posts BB 1 BB

Pre Flop: (pot: 1.4 BB) Hero has 7♥ 8♥

fold, CO raises to 3 BB, Hero calls 3 BB, fold, fold

Flop: (7.4 BB, 2 players) 3♦ 7♣ 4♣
CO bets 5 BB, Hero calls 5 BB

Turn: (17.4 BB, 2 players) A♠
CO bets 13 BB, Hero calls 13 BB

River: (43.4 BB, 2 players) 7♠
CO bets 115.6 BB and is all-in, Hero calls 79 BB and is all-in,

Large bets makes that his range should be polarized either a complete bluff or close to the nuts. I would therefor say that he probably does not have a Ax hand. Could AK make this play?

With what hands could he have made this play and make a huge bluff at the end with?
The most obvious is a missed club draw that semi bluffed both the flop and the turn.

With what hands could he have made this play and make a huge river over pot sized bet with?
AA-33-44 and perhaps a 56 which he decided to bet with pre-flop from the CO.

Here my thoughts:
What hand is putting the villain you on. You called pre-flop, flop and turn so you should have something.
I would be torn between calling and folding here. What is my opponent trying to achieve?
The only thing he can let me fold normally in this situation is a Ax hand that flopped some piece of the board (AK, AQ would probably 3 bet). My other holdings are either missed flush draws that will fold to any bet so why a big bet? My made hands 33-44-77 full houses and squads will not fold (AA would 3 bet). Then there is over-pairs to the flop that stayed on the turn bet yes that will fold to a huge over bet but the highest of then would 3 bet and the rest would fold to a 3/4 pot bet.

If hes a thinking layer I would happily fold to his bet, but is he a thinking player, stat wise I would say he is a thinking player, so a fold it is.

Villain pretends to have AA.
And put up a good show to support it.
Depending your table image....fold seems to have been the better option.
But with the call you'll find out if your set holds, or if your beaten by a boat.

trust you'll reveil the reality

It's the old let's throw out at action flop play brought to you by ...
Well by every online site out there anymore!
I'm guessing it's a newer online player, not a thinker and they have the the obvious AcE Seven offsuit?
It's really the only thing that makes sense? As then your dominated and the big shove at the end isn't a bluff it's a
Oh my God I made a full house!
I probably call here out of stubbornness, stupidity or curiosity? Pick one and we'll go with that? Again im pretty certain you lost the hand or it's wouldn't be posted? So I'll leave my wager on the old ACE rag?

If you think he had a single A or better wouldve folded the turn, the shove on the river looks like an AK desperate bluff. But could be someone getting excited by a house.

Bad play, dude. You were in a worst position than him. When he 3-bet you there were 2 options for you 4-bet or run. If you just pays he will know you don´t have a monster hand and he will be sucessful puting pressure on you due to his position.

Thx for all the comments, we learn every time ... he had 33