[Kurn, son of Mogh]

Well, first of all, it's profitable because you win the $44 pot over 90% of the time. But being a winning poker player is about extracting maximum vale from your winning hands (and giving up minimum downside on your losing hands)

So, lets look at your options and calculate the marginal value of each option to you.

If you check the turn and he folds to your river bet when he doesn't improve, you win $0 extra the 12 times you win, and lose $8 the one time you lose (we assume you bet the river and call his raise). The marginal EV of not betting the turn is -$0.62.

If you bet the turn and then bet the river regardless of what falls, you win $4 the 12 times you win the hand (we'll assume he folds when he misses his draw) [$48], and lose $12 the one time he improves (we assume you bet the turn, bet the river and call his raise) [$12] for a marginal EV of +$2.77 when you bet the turn.

Clearly, betting the turn with the intention of betting the river and not folding is worth slightly more than 1/2 bb more than checking the turn.

Note: this analysis does not consider $ already in the pot, it's simply an analysis of the marginal profit you make by betting the turn.

Why do you call his raise on the river? Because when he raises you're getting a minimum of 13:1 on the call and he's probably bluffing more than 7% of the time.