The continuation bet on the turn of 1/2 pot is fine. There is a chance the flush card was a scare card for opponent or he can have a weak flush and fears you have a higher flush. Essentially, you are making a defensive bet in that situation.

True weakness would be a complete check on the turn. On the other hand an observant opponent may be thinking semibluff/slowplay (you just never really know what the other guy is thinking) You are opening yourself to a big bet from your opponent that you are really not prepared to call.

The concept of betting pot or 1/2 pot is geared toward making your opponet make an incorrect call. On the flop the pot sized bet made it incorrect for him to call with a flush draw b/c he was only getting 2-1 on his money (discounting implied odds completely). On the turn, the draw got there so you are betting for information and trying to pick up the pot with the least risk which makes it unnecessary to blast the entire pot again.