Should I bet this a little harder?

[Siawyn]

I end up against a stack that is only half the buy-in...

PokerStars No-Limit Hold'em, $2 BB (8 handed) converter

Button ($209.10)
SB ($198.50)
BB ($200)
UTG ($252.55)
UTG+1 ($143.15)
MP1 <font color="#A500AF">(Villian)</font> ($99.80)
MP2 ($374.50)
Hero ($200)

Preflop: Hero is CO with K[img]/images/graemlins/heart.gif[/img], K[img]/images/graemlins/diamond.gif[/img].
UTG folds, UTG+1 folds, <font color="#CC3333">MP1 <font color="#A500AF">(Villian)</font> raises to $8</font>, MP2 folds, <font color="#CC3333">Hero raises to $22</font>, Button folds, SB folds, BB folds, MP1 <font color="#A500AF">(Villian)</font> calls $14.

I figured I didn't want to reraise TOO big because it's unlikely anyone else will be coming in unless they have a huge hand themselves.

Flop: ($47) 3[img]/images/graemlins/spade.gif[/img], 4[img]/images/graemlins/spade.gif[/img], 8[img]/images/graemlins/heart.gif[/img] <font color="#0000FF">(2 players)</font>
Villian checks, <font color="#CC3333">Hero bets $35</font>, Villian calls $35.

Thought process: With him being a shortish stack, I thought he might have something like TT/JJ/QQ here. If he had aces, then he was playing it perfect. But if I over-bet the flop here, he might get away from a smaller pair. If he's on the flush draw, I want to bet an amount that entices him to call, yet his stack size is tricky in that whatever he calls here, he's almost committed to the rest of the hand. So do you make it a push here?

Turn: ($117) 7[img]/images/graemlins/spade.gif[/img] <font color="#0000FF">(2 players)</font>
Villian checks, <font color="#CC3333">Hero bets $43</font>, Villian calls $42.80 (All-In).

I couldn't see myself folding here, so I'd rather not give a free card to a lower pair, especially one that holds a spade.

River: ($202.80) T[img]/images/graemlins/diamond.gif[/img] <font color="#0000FF">(2 players, 1 all-in)</font>

Final Pot: $202.80

Results in white below: <font color="#FFFFFF">
Villian has 6s As (flush, ace high).
Hero has Kh Kd (one pair, kings).
Outcome: Villian wins $202.60. Hero wins $0.19. </font>

I run into this problem occasionally when I am up against those half-stacks. I can't say I really had a read on this guy, hadn't seen him before, and hadn't been at the table for long. I'm just wondering on the EV of just open-pushing on a flop like that, or if my correct play was the one above.