You're right, birds don't get ill when moulting unless they are undernourished.
I think the weight loss may be linked to the breathing disorder. Are you able to open his beak and look down his throat?
A white cheesy deposit at the back, or any redness.
Ok, that probably rules out thrush/candidiasis. The most likely cause of his signs is a respiratory tract infection. Birds have a system of air sacs and hollow bones meaning that any lung infection can affect the whole body. I recommend you start him and his companions on a course of oxytetracycline, administered in the drinking water. If you bring him in to your vet they should be happy to prescribe this if they agree and the treatment is cheap, safe and effective.
In the meantime, keep him warm and his area well ventilated. Use a kettle to create steam if the area is dusty.
No problem. Please keep me updated with his progress - you can do this free of charge and ask follow-up questions via this thread. All the best, ***** *****