414 places paid, 850 players remain. This is a low stakes ($11) online tournament with a big field
Wondering if there's ever a world where I should raise this river:

Ante is 0.1bb
Hero in UTG with 42bb and JsJd, opens 2bb
Folds to unknown Villain in BB with 50bb, flats
Flop is Jc7s4d
x/x
Turn is Qc
Villain x, Hero bets 3bb, Villain calls
River is 2c
Villain leads for pot (almost 11bb)
Hero calls... but?

Thought process for each street:
Flop: Checking flop back since it's hard for V to have anything that would continue for a value bet + protects checking range IP

Turn: No longer blocking top pair as hard (only blocking QJ), 2 clubs on board so I bet for value and some protection, giving club draws the incorrect odds to continue and I am never folding to a turn x/raise

River: The villain leads for pot, don't know anything about him, just that this is an online lowstakes $11 buy-in. Obviously not thrilled that the 3rd club arrived on the river. If I had a read that V was a nitty player that never makes a big bet without a nutted hand I could be convinced this is an unfortunate fold, but I have zero reads on this opponent. I gave folding real consideration, since this is a low stakes tournament and I have no clue on how often this river will be bluffed. You could also say I got exactly what I wanted by checking the flop. I try not to go around folding sets, so I made the call this time - but I am wondering if I should ever raise for value here, even a min-raise. My gut tells me that any time I'm raising this river I'm only called when I'm beat, and maybe I get called by a worse set or 2 pair very rarely.

Will post outcome later

I wouldn't raise river. I'd guess this range is heavily weighted towards flushes or air so raising doesn't accomplish much.

You said flop you don't see him continuing with much when you have JJ - I think there are loads of hands they can continue with. Two overs, gutters, 2nd/3rd pair, 55 or 66, 65. If you specifically want to check JJ it's fine, but I'd prob be betting 75% pot with most of my betting range and I'd prob bet JJ for 33%.

River I'm never folding vs. someone who takes this line. Yes against some people it will only ever be a flush. But you will see a lot of KT/T9/T8/98/65 as well.

No straights out there, so we're down to a slow-played set, flush or the kinds of hands OJ mentions in his final sentences. If he got there runner-runner with some flush combo (A7?), or QQ, well, congratulations.

I think I bet flop a lot, and then bigger turn.

AP, river, I think I raise a lot of the time. especially if V is aggressive. With the flop x/x, you're really underrepped. Mix in some just calls when V is tight.

Flop is almost a pure range bet, betting the nuts for like 30% feels weird, but you also have stuff like Q9hh that would love to fold a random K or even A-high hand if your opponents don't defend well enough. You don't realize need to worry about protecting your checking range because on this board, you just don't have one.

If you check flop, you really want to bet bigger on the turn especially after BB checks again. This range will very often have a lot of marginal one-pair hands that we want to get as much money from as possible, especially as this board is a little more coordinated now. GTO will probably want you to be something like half, but I think 66-75% pot is pretty nice in that if your opponent has anything decent, like a Q or J, they're never going to fold to that bet. If they have backdoor clubs or even KT or T9, they're probably not going to fold. And even stuff like 88 or 99 is probably going to lookup at least one bet.

On the river, leading is really not a thing from a theory perspective. So I think this range is pretty much rivered clubs, a weird bluff or a marginal value hand not wanting to face a bigger bet. So this just becomes a question of whether we want to raise or not.

Because the BB can arrive here with backdoor flushes and the 2 isn't a card that completes a lot of other stuff for the BB unless it's exactly a hand like J2 or Q2, I tend to lean call because if we raise, it's unclear how many worse hands call. In a lot of ways, the BB has done our job for us because our likely bet size was going to be pot anyway, so taking the 11BB and not having to face a check-raise pile seems pretty good to me.

Outcome: Villain shows QsKc

I ran this spot through a solver and I agree with this for the most part. JJ is a hand that is allowed to check back about 7% of the time but yeah, this board will get bet with 95% frequency from IP. It also sized up the turn, most frequently betting with 2/3 pot but still overbetting about 20% of the time. I could have extracted more value since I only bet 1/2 pot (which the solver will still do about 5% of the time), but playing against a human I feel like if he's calling 1/2 pot he's probably calling 2/3 pot on this board.