If the duck is eating well while loosing weight, I too think it is likely worms.
I worm my fowl, be it chickens, turkeys or pigeons, with Ivermectin liquid form orally.
Designed to worm cattle. I do this twice a year. Early spring and late fall.
5 drops down the back of there throat so as not to get it down into their lungs.
And I know lots of people will raise hell about this idea. But I have been worming
horses, dogs (large and small), chickens, turkeys and pigeons like this for 45 years.
And I haven't killed one yet. I have a pair of pigeons 13 years old and still breeding.
Hell, holding the dropper in my mouth while grabbing the next bird I have accidentally
wormed myself a couple of times. No ill effects. LOL!