400NL - KQs OOP in rr pot flops nut FD

[Mat]

Villain runs 21/11/4 (242h), very straightforward, unimaginative poker.

Post-flop he's kinda nittish as I saw him take an eternity to call a 2/3 pot bet with set on river on a reasonnably safe board. I think his calling range to my 3-bet is pretty tight, but he probably calls with all his small pocket pairs too. I don't know if he 4-bets AA-KK.

Everest Poker No-Limit Hold'em, $2.00/$4.00 (HH Converter by Kreatief)

SB ($402.90)
BB ($407.90) (Hero)
Button ($339.00)

Preflop: Hero is BB with K[img]/images/graemlins/club.gif[/img], Q[img]/images/graemlins/club.gif[/img]
<font color="#CC3333">SB raises to $14.00</font>, <font color="#CC3333">Hero raises to $46.00</font>, <font color="#666666">1 folds</font>, SB calls $32.00,

Flop: A[img]/images/graemlins/club.gif[/img], 6[img]/images/graemlins/diamond.gif[/img], 9[img]/images/graemlins/club.gif[/img] ( $98 )

What's the best line ? Continuation bet or check with the intention of raising all-in ?
And what to do if I c-bet and he raises ? Should I push even though I'd be sure he has at least AK ?