Party Poker 1/2 Hold'em (10 handed) converter

Preflop: Hero is SB with [Kc], [Qd].
3 folds, Hero completes, BB checks.

Flop: (4 SB) [Jc], [3s], [Qs] (4 players)
Hero bets, Hero folds, MP1 calls.

Turn: (5.50 BB) [5h] (2 players)
MP1 checks, MP2 bets, MP1 calls.

River: (7.50 BB) [4c] (2 players)
MP1 checks, MP2 bets, MP1 folds.

Final Pot: 8.50 BB

Results in white below:
MP2 doesn't show.
Outcome: MP2 wins 8.50 BB.

Initial raiser was 30%/5%/1.0 (95 hands) , 3-bet raiser was 18% /0%/2.0
(45 hands)

What should I have done for 2 bets back to me?

Hmm...this is why I'm a proponent of raising KQo there, to get control of the hand, and build up the pot

One of them is clearly on a flush draw, but what might MP2 have?
QJ is a possibility, as is a weaker queen.
Or a flush draw and a pair is always a possibility as well

It's tough, but I think you can lay this down here, as you only have 5 outs to improve with

easy laydown considering the MP2's stats. what's confusing me is, how on earth someone has a 2.0 ag factor w/o raising PF, kinda odd if you think about it

Yeah, pretty easy fold in the face of a 3-bet. MP1's raise isn't much to worry about--yeah, he might be raising on an AQ or something, but he could also have a draw (Having the hindsight of the entire hand playing out, I'm guessing this is what he was on), or a weaker queen, or god knows what--but MP2 is bringing the goods if he's 3-betting.

ALSO: I agree that KQ is a raise-or-fold pre-flop hand. You really should've raised it out of the small blind, though I don't think it would change much in this instance.

I'll say this much, that is the perfect flop to CR from the small blind. This is why you sometimes just complete w/KQo. If it's only one bet the CR that bitch and only slowdown if you get a strong read on someone