I don't want to be the type of player that can't lay down an overpair or TPTK when the situation calls for it, but I'm having trouble knowing when to do so. I think I should have probably laid these kings down, but I'm not too sure.
Not enough hands on Villian to know his style of play for sure, but he did seem on the loose side.

Party Poker No-Limit Hold'em, $ BB (10 handed)

UTG ($56.95)
Villain ($49)
Hero ($65.3)
MP1 ($55.4)
MP2 ($48.65)
MP3 ($15.25)
CO ($49.25)
Button ($14.9)
SB ($45.75)

BB ($52.7)

Preflop: Hero is UTG+2 with , . MP2 posts a blind of $0.5. SB posts a blind of $0.25.
1 fold, Villain calls $0.50, Hero raises to $2, 3 folds, CO calls $2, 3 folds, Villain calls $1.50.

Flop: ($7.25) , , (3 players)
Villain checks, Hero bets $6, CO folds, Villain calls $6.

Turn: ($19.25) (2 players)
Villain checks, Hero bets $15, Villain calls $41 (All-In), Hero calls $26.

At this point I didn't know whether villain had a set, straight (I thought this was unlikely), or if he was just semi-bluffing with a draw.
Do you guys think this was a bad call?

River: ($101.25) (2 players, 1 all-in)

Final Pot: $101.25

Results in white below:
Villain has Qd 8d (high card, queen).
Hero has Ks Kc (one pair, kings).
Outcome: Hero wins $101.25.

This is a very read dependant play against a weak player, I think this is a very easy call. Against a good player, this is a borderline fold. Against a good player they have to know you have a big pair and they are pretty much saying they dont care. Against a bad player, well I dont know, i guess to some players top pair is a monster.

When he goes all in, the pot is $75 and its only $25 to you. Youre getting 3-1 on your money. No way I could fold there.

This is one reason it can alot of times be correct to check the turn in hands like these. I wouldnt do it here though with the flush draw out there.

for what it's worth, i thought he had [Td].

which, of course, be an easy call.

I would look at how good of a player is villain. If he's loose enough to play 78 UTG+1, if he has a win rate high enough that I would think he has a set or something else that has me beat. All in all, once you bet that much you have to call because of the pot odds.