50NL: Flopped low flush against station

Poker Room skin
No Limit Holdem Ring game
Blinds: $0.25/$0.50
9 players
Converter

Pre-flop: (9 players) Hero is BB with 2 :spade: 8 :spade:
UTG, folds, UTG+1 (poster) checks, 3 folds, CO calls, Button folds, SB calls, Hero (poster) checks.

Flop: 4 :spade: A :spade: 3 :spade: ($2, 4 players)
SB bets $0.5, Hero raises to $2.5, UTG+1 folds, CO raises to $4.5, SB folds, Hero calls.

Turn: K :diamond: ($11.5, 2 players)
Hero bets $7, CO raises to $14, Hero calls.

River: 2 :diamond: ($39.5, 2 players)
Hero checks, CO is all-in $13.3, Hero ???.

Results:
Final pot: $66.1

villain was 66/3/0.4. Can you put villain only on the flush? Villain's raise would be flush and set, no?

Why not go to war on the flop? Why not shove the turn instead of calling? This can be a set/straight a lot.

The issue I had was that going to wat with such a low flush and against a calling station was akward.
However, I agree, if I call the river I should have pushed the turn ...