$0.75/$1.5 200bbs deep. Extracting max value from rivered nuts

[Rasmus]

This is about 20 hands in. I have been raising a lot and he hasn't played back at me yet. I've 3-bet him once where he folded.

Full Tilt Poker
$0.75/$1.50 No Limit Hold'em Ring Game
2 Players
LegoPoker Hand Converter

<font color="black">Stack Sizes</font>
BTN: $290.85
Hero (SB): $306.3

<font color="black">Preflop:</font> K[img]/images/graemlins/club.gif[/img] A[img]/images/graemlins/spade.gif[/img] ($2.25, 2 players)
<font color="red">BTN raises to $4.50</font>, <font color="red">Hero raises to $13.50</font>, BTN calls $9

<font color="black">Flop:</font> 2[img]/images/graemlins/diamond.gif[/img] 8[img]/images/graemlins/spade.gif[/img] A[img]/images/graemlins/heart.gif[/img] ($27, 2 players)
<font color="red">Hero bets $20</font>, <font color="red">BTN raises to $65</font>, Hero calls $45

<font color="black">Turn:</font> 2[img]/images/graemlins/diamond.gif[/img] 8[img]/images/graemlins/spade.gif[/img] A[img]/images/graemlins/heart.gif[/img] [K[img]/images/graemlins/spade.gif[/img]] ($157, 2 players)
Hero checks, BTN checks

<font color="black">River:</font> 2[img]/images/graemlins/diamond.gif[/img] 8[img]/images/graemlins/spade.gif[/img] A[img]/images/graemlins/heart.gif[/img] K[img]/images/graemlins/spade.gif[/img] [A[img]/images/graemlins/club.gif[/img]] ($157, 2 players)

As I see it I have 4 options:
1) Value bet $80-$115
2) Value bet $115-$160
3) Overshove
4) Check raise

I think 1 works if he has a pair. I doubt he raises the flop much with a pair though. The only pair I think he could have is kings. He raises the flop with air and now has some showdown value once he hits the turn.

I really don't like 2 as I think I don't get enough value from pair hands and not enough value from better hands.

Overshove works good if he has an ace or better because he's calling like 99% of the time whereas if I just bet $135ish he might just flat call with trips no kicker. If he has a boat he's obviously calling.

How likely is he to check the turn behind with a weak ace? AT-AQ? Does he check turn behind with a set or two pair?
How often does he raise this flop with an ace?

Check raising could also be good I think. If he raises the flop with air and got scared of my call he might stab again at the river. How often does he have air on this river? Will he value bet if he has a king?