Fold preflop or at most cold call. KTo is too easily dominated.
Check behind on flop. you don't have a big hand but it has showdown value, the pot is large and you're not really folding much that beats you.
If you really insist on raising preflop and cbetting, i think you need to go ahead and double barrel the turn.
Folding the river is good. Any decent A beats you with better 2 pairs or a straight.
I think folding is weak here in sb vs bb situation. I fold 0% of Small Blinds opening into my Big Blind at 6max unless the guy is super tight and never stealing. I 3bet all sorts of stuff like 27o, etc just b/c the SB is usually opening super light in 6max games and I will have position postflop. I flat call here with the KT and most likely try to take it away postflop since, like u said, its easily dominated by villains calling range. Until a villain shows me that they are good enough to raise the SB and play a 3bet OoP i will just continue to hammer away at them.