Can you overfeed a copperband butterfly fish?

I know this is probably a stupid question.
I've had my Copperband Butterfly for about a year now and he has probably doubled in size since I got him and he LOVES to eat.
I don't think he would ever stop eating as long as I put food in the tank.
I haven't done it yet, but I was wondering if it would be a bad idea to keep feeding him (brine shrimp soaked in Vitality) until he won't eat anymore each time I feed. It seems he is always looking around for food and always picking at the rocks. I don't want to over feed my tank though, I already have a green hair algae problem, but it all turned brown a couple days ago, so I think it's dying, hopefully. Anyway, should I feed him as much as he will eat at meal time, or cut him off?

I have:
1 Dejardini Sailfin Tang ~ 2"
1 Blue Hippo Tang ~ 1"
1 Copperband Butterfly ~ 2-3"
1 Spotted Mandarin
1 Royal Gramma
1 Algae Eating Blenny
1 Firefish Goby
A pair of clowns hosting anemone

I feed them every day at dinner time, 2-3 cubes of the frozen brine shrimp soaked in Vitality for vitamins. (I give the tangs algae flakes first - the they will still eat the shrimp though)
All of the food gets eaten. And the Butterfly eats a lot and afterwards, all the other fish seem satisfied, but not the Butterfly, he still wants more, should give him more? I mean, obviously what I've been doing this far is working, he is happy, disease free, doubled in size, and best friends with my sailfin;D swimming side by side everywhere, even sleeping next to each other if you will. I'm only asking because if I can give him more food and it won't be bad for him, why not? I have pictures on my profile of my tank and all my fish.

 

I'd cut the fish off. I kept an Aussie CBB for several years, and once the food was gone, it was gone. In the wild, CBBs kind of pick all day, but unless you're home and can offer small, multiple feedings, whatever the fish can eat in a couple of minutes should be fine.

FWIW, our lionfishes will eat to the point of regurgitation if we let them (they are fed about 6 eye-sized food items 3x a week). They're always begging, even right after a meal.

Overfed fish often succumb to hepatic lipidosis over time.

 

Okay thank you, good to know. I will just keep doing what I'm doing.

 

Just keep an eye on the fish's weight...if it seems thin, bump up the feedings a bit. CBB's can lose weight quickly, but since you have a good feeder, you should be OK.