BB is a TAG playing 19/16, folding BB to a steal 77% of his hands.

I have K9 in the small blind, and it is folded to me. I have a 780 stack.

I raise to 19, he calls, with a 600 stack.

Flop comes (38)
I bet 30, he calls.

Turn (98)
I bet 66. He raises to 200.
Hero? Shoves, fold or call?
I called.

River (498)
I check he bets 250 (leaving 100)
Hero?

i would call because i suck at poker. i think though, it might be correct to lay down your top two in this spot, as i can't really see this being done by a hand that you beat. i think you're either up against a set or a straight. the way this hand was played i think probably a set.

this is tough. i think it's unlikely he has a straight here.

does he call PF w/ 85s? probably not.
does he call flop w/ T8? probably not.
would he take such a strong flop/turn line w/ KT? probably not.
i can't see him really taking this line with 75 or 65 either.

a set is very possible, though, as are lower 2 pairs, and bluffs, and maybe some one-pair hands that he's turned into bluffs, and maybe some bluffs that turned into straights. unfortunately for you his bet looks rather value-ish.

i don't know what the fuck to do here.....but i do know that i prefer shoving the turn. you get looked up super-light blind vs. blind.

Shove turn to keep yourself out of these spots...and for obvious value.