Begginer Looking for Advice on Turn Decision

I am pretty new to poker and was unsure whether I played this hand poorly. I would appreciate some advice, especially on my turn decision.

Playing 6 handed online 200BB effective and CO opens to 2.5BB, I call on BTN with 3h, 3c and it folds to BB who 3-bets small to 8BB (pot 24BB). The BB is agressive and likes to bluff.

CO calls, and I call.

Flop comes 4d, 9d, 3s

BB C-bets 16BB, the CO folds and I decide to raise to 54BB - my thought process here is that villian is clearly representing a strong hand like an overpair or nut flush draw so I should raise and get the money in as quickly as possible - BB calls

Turn comes 4s and BB checks - I am not super sure what to do here becuase now if villian has a flush draw I dont want to go all in and potentially fold out those hands and all the strong pocket pairs will probably be calling a jam on river so I check behind.

The river comes 4c and BB jams. My full house is now shite but I still beat all villans missed flush draws that get here. I fold, but idk if I played this hand correctly, especially my turn decision to check, how much of villians range is flush draws on the turn and does that justify checking behind to let them catch up? Also if a chunk of villians range is missed flush draws on the river, should I be bluff catching here or is too much of his range value?