Poker Stars, $0.05/$0.10 No Limit Hold'em Cash, 6 Players

SB: $13.50 (135 bb)
BB: $8.22 (82.2 bb)
UTG: $7.15 (71.5 bb)
MP: $10.55 (105.5 bb)
CO: $13.97 (139.7 bb)
Hero (BTN): $13.79 (137.9 bb)

Preflop: Hero is BTN with 4 5
3 folds, Hero raises to $0.30, SB raises to $1, BB folds, Hero calls $0.70

Flop: ($2.10) 9 Q K (2 players)
SB bets $1.40, Hero calls $1.40

Turn: ($4.90) 9 (2 players)
SB checks, Hero ??

Villain is
26/21, 23A%
6.9% 3bet (4/58)
16% 3bet from blinds (3/19)
45% cbet (5/11)
145 hands

Whats your line here?

I figure that this hand should be part of my 3b calling range pre? Probably the low end but still.

I figure I've got pretty close to the right implied odds to call the FD here but then I may be wrong here as well.

I'm just soo confused by his check here I figure this board hits his 3b pre range pretty hard so what can his checking range here look like?
TT-JJ, AQ, + the one combo of 99, and 6 combos of QQ-KK that he might decide to slowplay here so a decently sized bet should fold out 24/31 combos of that range. This could be way off though and he might not ever fold a pair or he might c/c his top pairs and AA on the paired 9.

Sorry I'm a bit fried right now so all that shit might not make any sense.

Thoughts?