Preflop: Hero is BB with

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1 fold,
UTG+1 raises, MP1 calls,
1 fold, MP3 calls,
3 folds, Hero calls.
Flop: (8.50 SB)

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,
(4 players)
Hero bets,
UTG+1 raises, MP1 calls, MP3 folds,
Hero 3-bets, UTG+1 calls, MP1 calls.
Turn: (8.75 BB)
(3 players)
Hero bets, UTG+1 calls, MP1 calls.
River: (11.75 BB)
(3 players)
Hero bets, UTG+1 calls, MP1 folds.
Final Pot: 13.75 BB
Would you have led out on the river or check-called? I am thinking that the check-call is a better move. If he was chasing a draw he is going to fold anyways, so I am more likely to lose that bet to a better hand than to win a bet.
I like how I played every other street, but I am not sure about the river. I suppose he might be calling down with a TT or something but it seems doubtful.