Check or bet? And what about sizing?

First hand @ table

$0.25/$0.5 No Limit Holdem
6 players
Converted at weaktight.com

Stacks:
UTG sandbanken ($41.93)
UTG+1 Kenzoo ($46.49)
CO IBustedYou ($70.13)
BTN 100479 ($23.35)
SB doss ($109.16)
BB Hero ($50.00)

Pre-flop: ($0.75, 6 players) Hero is BB :ad: :kd:
3 folds, 100479 calls $0.50, doss calls $0.25, Hero raises to $2.40, 100479 folds, doss calls $1.90

Flop: :3s: :8h: :4d: ($5.80, 2 players)
doss checks, Hero bets $4, doss calls $4

Turn: :ks: ($13.80, 2 players)
doss checks, Hero ($43.60)?

why would you do anything but bet here, $10 is fine.

Please always bet in this spot.

Yeah vs. unknown I'd always bet 10 looks good.

Vs. regulars its always a bet obv. as they know you barrelling overs so they look you up lighter & balance but there is an argument that against weak players you should just barrel K/A as a bluff and check behind in this spot and Bet river. (The A/K is like the death card for them just like regulars seem to get overly scared when the third flush card hits on the turn.)