AJ makes 2 pairs in 3bet pot

Hi,

What do you think of this zoom hand? Vilain is unknown, 0/0 on 5 hands

Preflop is a standard 3bet defense

Flop : I hit the flop super hard, i decide to check and try to get value from worst or bluffs from vilain on the turn
Turn : I just call to try and get another bet on the river
River : Here is what i think is the biggest mistake of the hand. In retrospective, as played, i think i just better call the bet and go to showdown. He doesn't have a lot of hands in his range that will call my push and get beaten. With the 3bet defend, he can have ATs+, 99+, KQo KQs, sometimes KJ if he is a bit loose. Basically, in his push calling range, i probably only beat AT and sometimes AK if he is a bit spewy (but we don't know).

This kind of spot is usually where i lose all my money because i want to get the max in

What do you think of my line of thinking?

Thanks!

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

BTN: 143.4 BB
SB: 126.6 BB
BB: 100 BB
UTG: 96 BB
MP: 117.4 BB
Hero (CO): 117.8 BB

SB posts SB 0.4 BB, BB posts BB 1 BB

Pre Flop: (pot: 1.4 BB) Hero has J♣ A♠

fold, fold, Hero raises to 2.4 BB, fold, SB raises to 9 BB, fold, Hero calls 6.6 BB

Flop: (19 BB, 2 players) 4♣ A♦ J♥
SB checks, Hero checks

Turn: (19 BB, 2 players) T♣
SB bets 9.2 BB, Hero calls 9.2 BB

River: (37.4 BB, 2 players) 6♥
SB bets 26.8 BB, Hero raises to 99.6 BB and is all-in,