KQs in the BU — but I think I botched it post-flop

I think you could raise the turn, worse hands that may call could be some Ax, A3 (possibly all combos). Villain should be 3-betting his AK,AQ so I mostly take those out from his range pre. I'd probably raise turn and fold to a 3-bet on the turn. River is a good fold because of the bet and the re-raise. BB can have all JT combos and he bet nearly 2x pot so its pretty polarizing towards the nuts. Depending on the player type some people might spaz river as BB with a bunch of worse two pairs since he can call pre with a bunch of junk but without reads and facing the large river bet I like the fold. Also I don't mind just the turn call if you think SB's range is two pairs+ since it would be hard to be called by worse when we raise, so overall I think the hand was played fine, maybe we could raise turn but not a huge deal imo.

I completely agree what Casey55 said. Raising the turn could arguably the better play but would also make you more pot commited with a harder to make dicission OTR. It's very unlikely he would bet so heavy with a worse hand on that board. A better 2-pair, straight or set either way you are beat.

I would consider to make a thin value Cbet on the flop with middle pair top kicker.
You can easy represent a ace and the ace isn't to likely in defending ranges on both villains.
Turn is as played a tricky card with JT out there, but I would try to protect my hand and raise for thin value as well to like 15bb.
River is most likely a fold with 2 pair against a bet and a raise in front of you, but it's close on NL2. It could be that villain will over play weaker 2 pair hands.

Cheers,
SDK1987