Villain is unknown. Buys in full stacked, so no obvious indication of fishiness. When villains take over the initiative like here I tend to give them a lot of credit for a strong hand; maybe too much. I'm scared of raising, thinking A2, 67, and bigger sets are quite possible here. I'm never folding of course, but I'm wondering if I'm losing value here by not raising. Since he calls pre I don't put many overpairs in his range, save perhaps JJ. That (maybe) and 2 pair hands I suppose I can elicit calls from if I raise. So, 16 combos of A2, 16 of 67, 3 of 55, 3 of TT, and 3 of 44 is 41 combos in total that have me in bad shape, and there are only 6 combos of JJ, none of 53s, 1 of 43s, and 2 of 54s, so 9 combos total, that may call a raise with me ahead. Calling down ok or am I too conservative (e.g. by excluding random oesd and maybe even gut shots?) in what I may be called with by an unknown and do I miss value here?

BTN: $2.00
SB: $1.98
BB: $2.00
Hero (UTG): $5.91
MP: $2.83
CO: $2.95

Pre Flop: ($0.03) Hero is UTG with 3 3
Hero raises to $0.06, 4 folds, BB calls $0.04

Flop: ($0.13) 5 T 3 (2 players)
BB checks, Hero bets $0.08, BB calls $0.08

Turn: ($0.29) 4 (2 players)
BB bets $0.14, Hero calls $0.14

River: ($0.57) Q (2 players)
BB bets $0.55, Hero calls $0.55

Raise turn vs that sizing and an opponent that is c/c flop and leading turn.

OK - so in your experience x/c F lead T is generally indicative of a weak player?

FYI - he had QTs, so in this case you're surely right!

Raise the turn. Not a whole lot of players at this level like laying down top pair, and those players definitely aren't folding 2 pair here.

Most players aren't taking this bizarre line with anything that beats you.

It's not a bad play if it improves your range relative to villains (your's) but I wouldn't give 2NL players credit for that and would just raise my set and go from there.

Could you (or someone) give an example of a generic hand example / situation where x/c - lead is a good play, if you're the oop player in a HU pot? When you hit the flop very hard and villain cbets F a lot but not much on T maybe?