This is really easy. Bet the max amount that you think villain will call with a range that you have more than 50% equity against. You bet too small on the turn.
If you don't expect villain to fold a K on the river then it's easy jam (most 42VIPIP players doesn't fold TP even if you overbet). Betting small so you can b/f is non-sense if you have over 50% equity vs his calling range putting more money in = higher EV. Don't c/c in these spots since by doing that you are guaranteed to not get value from the marginal part of his range and pay off 100% of his range that beats you.
Villain is passive, i.e. he invests money only when he has something. He folds his QT on the river, Calls his Kx and raises his Jx. The thing I don't want to do on the river is showing weakness by checking or betting too small. He might think I don't have much and play the river aggressively. The other thing I don't want to do is shove. If I put villain on QT, any Kx and any Jx, I have 60% equity. I don't think blindly shoving is a +EV thing to do. Judgment has to be used too. So my best option is to figure out a good amount to bet that will say to villain that I mean business. And if I get raised, then I'll know 100% I am beaten. If I get called, what's left of his stack that I would have gotten with a shove but didn't, I'll get later.
Here is the hand.
Poker Stars $0.02/$0.05 No Limit Hold'em - 6 players - View hand 1744633
DeucesCracked Poker Videos Hand History Converter
Hero (UTG): $14.66
Pre Flop: ($0.07) Hero is UTG with A A
Hero raises to $0.20, 1 fold, CO calls $0.20, BTN calls $0.20, SB calls $0.18, 1 fold
Flop: ($0.85) K J J (4 players)
SB checks, Hero bets $0.60, CO folds, BTN calls $0.60, SB raises to $0.78 all in, Hero calls $0.18, BTN calls $0.18
Turn: ($3.19) 2 (3 players - 1 is all in)
Hero bets $2, BTN calls $2
River: ($7.19) 3 (3 players - 1 is all in)
Hero bets $4, BTN raises to $8, Hero folds
Final Pot: $15.19
BTN shows K J (a full house, Jacks full of Kings)
SB shows K 5 (two pair, Kings and Jacks)
BTN wins $11.50
BTN wins $3.06