Check turn? River sizing?

***** Hand History for Game 1111111111 ***** (Poker Stars)
$5.00 USD NL Texas Hold'em - Wednesday, October 22, 08:10:21 ET 2014
Table Monachia (Real Money)
Seat 1 is the button
Seat 1: Player1 ( $13.01 USD ) - VPIP: 31, PFR: 24, 3B: 11, AF: 3.8, Hands: 85
Seat 2: Player2 ( $8.85 USD ) - VPIP: 24, PFR: 13, 3B: 6, AF: 5.7, Hands: 85
Seat 3: Player3 ( $15.30 USD ) - VPIP: 69, PFR: 36, 3B: 12, AF: 1.3, Hands: 83
Seat 4: Player4 ( $11.89 USD ) - VPIP: 16, PFR: 9, 3B: 3, AF: 1.5, Hands: 117
Seat 5: Hero ( $8.86 USD ) - VPIP: 23, PFR: 18, 3B: 5, AF: 2.7, Hands: 23568
Seat 6: Player6 ( $5.00 USD ) - VPIP: 20, PFR: 12, 3B: 0, AF: 0.0, Hands: 41
Player2 posts small blind [$0.02 USD].
Player3 posts big blind [$0.05 USD].
** Dealing down cards **
Dealt to Hero [ Td 9d ]
Player4 folds
Hero raises [$0.20 USD]
Player6 folds
Player1 folds
Player2 calls [$0.18 USD]
Player3 raises [$0.95 USD]
Hero calls [$0.80 USD]
Player2 folds
** Dealing Flop ** [ Ks, 6d, Kd ]
Player3 checks
Hero bets [$1.00 USD]
Player3 calls [$1.00 USD]
** Dealing Turn ** [ 8s ]
Player3 checks
Hero checks
** Dealing River ** [ 7d ]
Player3 checks
Hero bets??

BB is a confirmed fish. The only hand I can remember seeing him 3bet was 54s.

BB stats 70/37/68/14//11.8/45/-

Layout vpip/pfr/steal%/Fsteal%/3bet/cbet/fold to cbet

Upon review I think I like betting the turn more than check. I think it's unlikely I'm getting raised and I have a tonne of outs, plus I get to build a pot for the river.

Thoughts on turn play? Sizing suggestions on river?

Definitely bet the flop with his low-ass c-bet percentage (even though I'd recommend a check against an unknown).

On the river, you can probably go as much as 1.25x the pot without affecting his call frequency very much.