I don't really play 50nl, so I've got no notes on the player, he seems pretty solid.
Reason I say is it a check on the river, because he can't really call with worse as the board has ran out.
I have pocket 3's OTB, £38.83 at the start of the hand.
It folds round the player on my left who min raises to £1.50, I call, BB calls.
Flop;

It checks round to me, I bet £3.56, BB calls, other player folds. Pot is £11.87.
Turn,

, I bet £8.90 villain calls, pot is £29.67 I have £25 behind. Think I should have prob bet a bit more on the turn.
River is

Opponent checks.I jam. I think this could be a check behind, maybe? Only draw that has come in is 46. He can't really call with worse?
Villian had

.
Pretty confused by this HH.
You say it folds round to the player on your left.... the person on your left is the SB. Do we assume you mean 'right' as opposed to 'left'??
Also you say this player min-raises to £1.50? You're playing 50nl... a min-raise is to £1.00
Dependent on this, what is pot on the flop? Assuming it's ~4.50 then your sizing is fine.
If anything your sizing on the turn is a bit big... you want some calls from some marginal hands, seems like he has a pretty weak hand given he's c/called the flop, but obviously on a 2-tone I wouldn't bet really small. Anywhere £7-9 is fine.
River seems like a pretty clear jam. This river gives villain some 2-pairs, you'll get hero calls from some 1-pair hands given a lot of draws bricked and you're not repping many legitimate hands.
If you think you're never getting called by worse you're either playing in some hilariously nitty games where people never bluff, or you're perception of how wide people call needs some more thought. I'd suggest at 99% of 50nl tables you'll find jamming here is a very +EV play... checking you'll just miss out on a load of value a lot of the time.