This is a hand I played about three and a half years ago, so apologies for the absence of auto top-up, and the presence of Full Tilt...
I must have more recent hands that are similar, but don't have them marked. I'm not sure what to do if this comes up again though, so, line check please?

Full Tilt - $0.50 NL - Holdem - 8 players
Hand converted by PokerTracker 3

BTN: $97.00
SB: $27.60 - 39/7/2, over 44 hands
BB: $11.25
UTG: $17.05
Hero (UTG+1): $26.70
MP: $33.90
MP+1: $10.00
CO: $9.50

SB posts SB $0.25, BB posts BB $0.50

Pre Flop: ($0.75) Hero has K K

fold, Hero raises to $1.50, fold, fold, fold, fold, SB calls $1.25, fold

Flop: ($3.50, 2 players) 5 J 3
SB checks, Hero bets $3.00, SB raises to $12.50, Hero raises to $22.00 [misclick?], SB raises to $26.10 and is all-in, Hero calls $3.20 and is all-in

Pre-flop is standard (except that only one person has a significant amount of money on the table, oops).

I c-bet on the flop, hoping to just take it down. Villain check-raises (as he had done twice already in this session), and looks committed.
I decide to commit as well, hoping he has a non-club jack...

Was my line correct?
What if stack sizes and/ or stats were different?

Is this more "don't go broke with one pair" territory?
(What about if I had the king of clubs - would a 3-bet then be OK?)

well as played given its 50bb stack, bet/c all the time.

100bb deep, I b/f fold, we only have one card to improve our hand strength.

While I'm not contesting your conclusion, I can't resist pointing out that if we do actually need another K, the only hand against which the K is not good is AAx.

?????? What????

err, what about all he other clubs he may hold?

so you remember this after 3 years? or did you rly go through the whole session and check it? I mean.. whats the point of this?

and btw its pretty easy b/shove 50bb deep..

We all remember our bad beats

If he holds any other clubs then we're either already ahead and don't need another K to improve, or we're way behind to a made flush.

still not sure I understand your first post.

You have only invested 3bb in the hand. Why would you want to get it all in, where your opponnent is the kind that can have virtually any crap (like J3o or 10 2c). I would wait for a better spot.

This is all fairly irrelevent nit-picking, but just to clear up.......

He's saying that if we need to hit a K then the K is good for us.

Consider the following:

1) We're ahead and don't need a K
2) We're behind to flushes and both our K outs are no use (except for runner-runner)
3) We're behind to sets, in which case both our K outs are good

At no point are we only drawing to one out.

Anyway, now that nonsense is sorted out, for 50bb it's an easy b/c.

This is 100% incorrect thinking. The amount of money we have invested in the hand is irrelevant. What's important is the pot size, our equity and his range.

Also, if he's the kind to have Tc2c or J3o, then he's also the kind to have AJo or Ac4c here. Think about his range as a whole.

not sure if its level or not.. but this is not a badbeat and hands like this are very common in nlh so Im wondering why is he remembering that.

did the wink not help?