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Boss $25.00 No Limit Hold'em - 6 players - View hand 1785990
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BTN: $50.77 - VPIP: 23, PFR: 16, 3B: 2, AF: 3.8, Hands: 283
His fold to 3B is 43%.

Pre Flop: ($0.37) Hero is SB with K K
2 folds, CO raises to $0.75, BTN calls $0.75, Hero raises to $3.25, 2 folds, BTN calls $2.50

Flop: ($7.50) 5 A 4 (2 players)
Hero bets $3.75, BTN calls $3.75

Turn: ($15.00) J (2 players)
Hero ??

What should we do here on the turn? Should we be check folding or calling a half pot bet?
What if he bets 3/4 of the pot - should we fold then? We probably don't have the implied odds because he might not pay us off if we hit our hand. What about betting ourselves - half pot for example? But the problem is if we get raised we have to fold out our equity.

Thanks for the help

I would c/f. We don't have the nut FD and villain is not folding an ace. He could easily have 2p now or a set of jacks. TT-99 are folding so the only hand we can get value from is QQ with a heart.

Sorry, you are right, we don't have the nut FD, I confused the hand with a similar one.
Yeah, we should be folding, I agree.

Analyze it step by step:

1. What is his range on CO?
2. What is his Fold to 3-Bet and 4-Bet? Use them to estimate his Call to 3-Bet (100% - Fold to 3-Bet - 4-Bet)
3. [1] Range on CO * [2] Call to 3-Bet = his most likely range on the flop
4. Check out how range [3] hits this flop (use PokerStove)
5. How do you think he plays here with lower pairs like 99-QQ?
6. Figure out whether a c-bet has a positive EV (folding is always 0EV)

Villain has very high AF (3.8), which indicates he doesn't like calling (down) too much. This also means that his calling frequency with hands like, say, 77-JJ on this board is very low, therefore cbetting doesn't bring you much value except for winning dead money in the pot. Flop cbet is probably slightly EV+, but flop check-call is imo much better as it costs the same as cbet but it induces some bluffs.
Against such player you should either:
a) turn your hand into a bluff and triple barrel (assumptions: your image is clean + villain is not a hero-caller)
b) check-(likely call) flop and evaluate turn.

Notabene: Villain seems to have a wide preflop calling range so your Fold Equity when triple barreling is high on the river as he might have many weaker Ax + if he has something strong he's likely to raise (as his stats suggest).
Turning your good bluffcatchers into bluffs is not necessary at 50nl and I'd still go for plan b) here though.

I would c/f here on the turn. Even if we hit our flush we don't even know if villain is going to pay us off....Also we can't rule out the possibility he might have AK, AQ, AJ, AT with the A of hearts.....I know c/f with KK sucks but this is not a good spot OOP.......I don't think c/b on the flop is a good idea....We need to know where we stand in the hand, if he calls our flop bet then he probably has an A and won't fold it, or has high over cards with a heart.