do you not have reads?  if not, that's probably the biggest problem here.  watch ph33rox's videos for some good discussion of generating reads from early hands.
 
the "standard" river thought process is that it's a very clear fold because you shouldnt be ahead of any of his value raises and it's really hard for him to get here with air that he wants to use as a bluff since he called a few streets, there was no flushdraw, and ppl dont tend to bluffraise overbets anyway.  i'd be interested to hear why anybody would think this is anything other than 'easy fold' on the river readless
 
other than that, your betsizing is weird and probably not good on every postflop street.  i hate to give overly-general advice, but you might just want to stick with something like 1/2pot flops, 2/3pot turn and river for all your bets unless you have a good reason to deviate.

effective stacks: 1210   Blinds:10/20
this hand comes down to how your playing a certain hand range on the river spot vs villains total hand range:
Effective stacks:60.5BB deep... essentially ur deep stacked 
Dealing to SithJarr1: [Kd, Kh]
SithJarr1 raises 40 to 50
thunder12645 calls 30 
--- Dealing flop [5h, 3d, 2c] (100) 100=5BB
remaining stack: 58BB
board texture: this board is highly coordinated if villain was flatting you with low cards... hands like A4,4X,22,33,55,34,45, are all likely hands in villains flatting hand range....
but tht shouldnt deter you from betting flop...... your betting here for value vs mid  pocket-pair hand range5X,3X, 4X SD type hands, and overcard floats, thts in villains likely flop calling range. i dont hate 80, but too big imo, and villains continuance range tightens, due to ur big flop c-bet, i would personally bet something like 60, where i allow villain to call with a wider hand range
thunder12645 checks
SithJarr1 bets 80
thunder12645 calls 80
--- Dealing turn [7d] (260)=13BB
effective remaining stack:54BB
essentially your still not pot commited to this hand....
thunder12645 checks
SithJarr1 bets 100
i disagree with your bet sizing... i think ur giving villain odds to outdraw u.... your basically pricing him to call. If villain has a draw, he definetly is getting the implied odds to outdraw you here....
now with the 7(d), the board has become more coordinated.... with the inclusion of FD, i would bet bigger around 150-170 for equity protection and charging value vs villains FD+SD hand range
thunder12645 calls 100
--- Dealing river [Js] (460)=23BB 
Remaining effective stacks:49BB
thunder12645 checks
SithJarr1 bets 500
thunder12645 raises 1000 to 1000
I dont understand the river overbet???
what do you accomplish here, and what hand range is villain going to call you down with. If in fact he does call you, it probably has you beat with some kind of 2-pair hand range.....
Imo: KK here is only a marginal hand,,, thin value vs villains 1-pair bluffcatching range. and if in fact villain CR shove on you, you can still bet-fold while having around 30-ish BB left...
its obvious  your not beating any of villains value shove here, with your 1-pair hand range......
view the river spot in terms of relative hand strength, as opposed to actual- hand strength.....
Imo= villain rivered u with some type of goofy JX 2-pair, or he had the nut straight the whole way... since i dont think villain wouldve check called with 2-pair on turn, on such coordinated board,,,, he wouldve raised for protection there.......................