Pre Flop: ($0.75) Hero is SB with 9 of hearts Q of hearts
UTG raises to $1.75, CO calls $1.75, BTN calls $1.75, Hero raises to $4.50, 1 fold, UTG calls $2.75, CO calls $2.75, BTN calls $2.75

Flop: ($18.50) J of hearts 7 of spades 3 of hearts (4 players)
Hero bets $15.50, UTG folds, CO calls $15.50, BTN folds

Turn: ($49.50) 6 of clubs (2 players)
Hero bets $23.00, CO calls $23

River: ($95.50) J of spades (2 players)
Hero checks, CO checks

so i played this wierd spot today in my session and could not make up my mind on the river so i checked but anyways heres my thougth procces: since my play preflop play i decided to cbet because of
1. theese table was way overfoolding flops in past 3bets pots
2. i thougth that my range was good for cbeting this flop and in general this flop miss random cold calling fishes? correct my if im wrong!
3. on the turn i thougth i could barrel big once more because of getting the CO player to fold his better flush draws, and maybe som low pp
4. so when i end up here on the river i thougth that he never really would fold to a shove because of how the hand was played so i checked assuming his range consisted of: AJ J7+ 33, 77, 78hh QQ TT KQ,
So for the question, should ive played it in any other way? if so? why ?