Villain is the donk here. On both the flop and turn you have correct pot odds to draw to the nuts. With 12 outs you have about 1/4 chance of hitting next card, so folding to a bet of less than 1/2 pot would be to giving away money.
I wouldn't raise KTs from the BB though, it's not a very strong hand and certainly not one that you want to build a large multi-way pot with out of position. On the flop you might consider leading out strong since you're not really afraid to get all-in. But out of position against 3 opponents who may not know how to fold I would probably prefer to draw with nice pot odds and implied odds. Once UTG bets weak and the other two players fold check-raising could work though, pushing would only be a slight overbet.