PokerStars 2/4 Hold'em (6 handed) Hand History Converter Tool from FlopTurnRiver.com (Format: FlopTurnRiver)

Preflop: Hero is UTG with 7, 7. CO posts a blind of $2.
Hero raises, 1 fold, CO (poster) calls, 2 folds, BB calls.

Flop: (6.50 SB) 6, T, 8 (3 players)
BB checks, Hero bets, CO calls, BB folds.

Turn: (4.25 BB) 9 (2 players)
Hero bets, CO raises, Hero 3-bets, CO caps, Hero calls.

River: (12.25 BB) A (2 players)
Hero checks, CO bets, Hero calls.

Final Pot: 14.25 BB

Very good.

You can't play it any softer than that.
No worries.

We are only afraid of J7 or QJ.
And Villain may think it is unlikely we have a straight since our preflop raise from UTG does not suggest we have the necessary cards to make one.
In that case, it is possible he is capping with a lesser hand (2pair?)

That possibility may be thin.
And the Flush card just hit the river.
So no reason to push any more.

You probably played it the only reasonable way.

--CM