Not so much a bad beat, but a hilarious showdown!
Full Tilt No-Limit Hold'em, 2.25 Tournament, 15/30 Blinds (8 handed) - Full Tilt Converter Tool from FlopTurnRiver.com

Hero (UTG+1) (t3310)
MP1 (t1455)
MP2 (t3020)
CO (t1350)
Button (t1455)
SB (t2910)
BB (t1485)
UTG (t1500)

Hero's M: 73.56

Preflop: Hero is UTG+1 with K, Q
UTG bets t90, Hero calls t90, 5 folds, BB calls t60

Flop: (t285) 4, K, 4 (3 players)
BB checks, UTG checks, Hero checks

Turn: (t285) 8 (3 players)
BB bets t285, UTG calls t285, Hero raises to t1425, BB calls t1110 (All-In), UTG calls t1125 (All-In)

River: (t4500) 3 (3 players, 2 all-in)

Total pot: t4500

Results:
BB had K, 10 (two pair, Kings and fours).
UTG had 4, 4 (four of a kind, fours).
Hero had K, Q (two pair, Kings and fours).
Outcome: UTG won t4500

I don't like your play on ANY street here.

You're looking at a raise from EP, while your holding KQo in EP. You can't call here. I fold this 98% of the time, and raise it the other 2. Raise it to about 175 +/- if you're going to play, and then if they raise you again, you can get away from it, but they will likely/hopefully throw away a lot of hands that might have you dominated, but probably not.

Why the hell are you checking on the flop? You're last to act, not like you can check raise this. Theres a paired board, and a flush draw. So now you're letting the 89s BB that was priced into seeing the flop with your weak ass PF call get a free look at a flush draw. WTF. Pound this now. 200-250 right now. Let's see what happens.

Turn, well now your fucked, by not getting info earlier in the hand, you are screwed here, as they have now given themselves odds to call pretty much anything. So you bet the only amount they DONT have odds to. So the only hands that will call this have you beat. And the only reason the KT called was because he was getting > 2:1 with top pair on a weird action hand, so he had odds by that point.

So you blow > 1/3 of your stack on a hand you had no business playing to start with, and had multiple opportunities to minimize the damage.