^^ This line isn't much good against a set because you shouldn't be giving free cards and you're losing a ton of value you could have got on the turn (but then you don't know that your opponent has a set unless you show down). The basic line that you can't go far wrong with is potting every street, although it depends on how aggressively you would play other hands, and it's OK to mix it up occasionally to stay deceptive.
On the turn here, you actually gave your opponent correct odds
to call with a set, which can't be good. He has 10 outs from 40 unknown cards to beat you, giving him 25% equity. So your bet amount X on the turn into pot P, has to be at least the value given by
X/(P+2X) = 25%
(1-0.5)X = 0.25 P
X = (1/2)P
So your opponent can profitably
call up to half pot on the turn from pot odds
alone, i.e. with $33 in the pot after his turn bet and your call, you have to raise it at least $16.50 more. Raise it $11 like you did, and it's costing him $11 for a 25% chance to win $44, so his EV is 25%*$44+75%*(-$11) = +$2.75, which must therefore be -EV for you.
You have to think about implied odds as well however, and how much you're going to call if the river pairs the board and he bets. You're probably not going to get away from it unless he bets more than half pot. So assuming he'll get paid off for half pot if he hits on the river, and check-folds anything else,
25%(P+X+0.5*(P+2X)) = 75%(X)
(1/6)P+(1/2)X = (3/4)X
X = (2/3)P
So really he's break-even, assuming he gets paid off, for anything up to a two-thirds pot-sized raise, in this case a $22 raise to $30 on the turn. But, you need to make it unprofitable
for him to call, so you need to raise more
than $22 on the turn. This way, if he folds, you have the same EV as if you raised $22 more and he called, BUT if he calls, that becomes even more profitable for you. In practice, people just mash the pot button rather than making a raise between two-thirds and full pot.
Of course you can't just put him on a set here and it may in fact be more profitable vs his range
, which includes many worse flushes, to bet smaller. Also, you may be able to make a small suck-bet if the river blanks, as discussed in previous posts, which would reduce the amount to bet on the turn slightly.
The short answer, however, is bet big on flop and turn. On the river, if your opponent has a set, he's unlikely to pay you off at all if he's any good. (You seem to have been lucky and have caught a live one...) The most profitable thing versus his range, as Rob says, is probably betting quite large and hoping to be paid off by a worse flush. Funnily enough, if you're putting him on a flush rather than a set, you played this hand OK!