Poker Stars $0.50/$1 No Limit Hold'em - 6 players
The Official 2+2 Hand Converter Powered By DeucesCracked.com

MP: $62.85
CO: $107.35
BTN: $101.75
Hero (SB): $117.40
BB: $111.05
UTG: $127.85

Pre Flop: ($1.50) Hero is SB with K K
1 fold, MP calls $1, 2 folds, Hero raises to $4, BB calls $3, MP calls $3

Flop: ($12.00) 4 4 9 (3 players)
Hero bets $7, BB raises to $20, MP folds, Hero calls $13

Turn: ($52.00) 6 (2 players)
Hero checks, BB bets $26, Hero calls $26

River: ($104.00) T (2 players)
Hero checks, BB bets $61.05 all in, Hero calls $61.05

bb is 27/21 with 13% 3bet over 360 hands, is my line ok here? i dont know what hands is he raising the flop with, and i think he doesnt flat any 4 preflop unless he didnt saw the limper, should i include A4s 45s in his range?

if there's a limper I'd flat A4s

Is raising the flop here bad because he folds his bluffs? I think we have to fold the river as disgusting as it looks. I just don't think he has a 9 or a bluff that often.

Stats are pretty loose; given theres a limper you're not far off to assume that Villain can hold a 4 here (and not just A4 and 45).
But I see no reason for him to raise that flop given that your both aren't even deep unless he specifically puts you on an overpair which is a small amount of the time given its a BvB situation essentially. More likely he would be bluff raising here and since there are no draws I like the line you took.
His turn bet is suspicious, betting half pot looks like he's setting up for an easy river shove, but I can't see us folding the river after we've put in almost half our stack. Imo folding could be the right move here, but in game I would probably play it the same as you.

\Whats the stats on MP? That's important here

never folding... if he isn't retarted he is flatting flop with hands that beat you, so he can keep the fish in the pot.

YETI principle applies - raises on dry boards are usually bluffs - and a guy who 3 bets 13% is aggro enough to overplay the smaller pairs too. Do we have his raise flop stat?

I would be more worried about 66 than anything else (assuming a 13% 3 better would have 3 bet AA-99).

Think you have to stack off on river getting almost 3:1 - $61 for a $230 pot.