Hi guys. My name is Kat, and I am a board eligible Veterinary Technician. I am NOT a Veterinarian, and I cannot Diagnose, but I have a very large amount of knowledge about many species of animals and specifically quite a bit of medical knowledge. Once I pass my board in about 90 days, I will be the veterinary equivalent of an RN for humans.
Actually- In a tank situation, I would be worried about the other fish getting sick, especially if it actually is white spot disease. I would keep an eye on them and consult a veterinarian who sees exotics if you see any signs of disease in the other tank inhabitants.
I am sure your veterinarian checked things pretty well, but be sure they checked the urine as well, weight loss despite a healthy appetite is also one of the cardinal signs of feline diabetes mellitus, though I agree that Hyperthyroidism would be my first concern. I highly doubt that a vet would have missed cancer of the mouth. Cats are obligate carnivores, so definitely make sure you are feeding a high quality food with a high protein content.
Typically birds do not just fall off of a perch for no reason. One major thing to remember(that has been mentioned, but I will reiterate anyway because I really think that this is the case with this bird) with birds is that the vast majority of our pet birds are prey species. This means that if they were in the wild, showing any sign of weakness or sickness means that they will quickly become someone's lunch. Because of this basic instinct of survival, they will hide all signs of illness until they are so sick that they cannot continue to do so. There are any number of things that could have happened to cause sickness.
A few questions so that I can get a better idea of what may have happened. Where in the house was the cage situated? Near the kitchen? Near any windows or doors or in the path of a draft? Are/were there other birds in the house? if so, what kinds, and how close were they housed? Are/were any of them showing any signs of illness? Often the first signs of illness in a bird include the 'fluffing' of feathers, sleeping a lot, listlessness, and/or a dull appearance to their eyes. If they were housed near the kitchen, do you use teflon coated cooking pans? If they were housed near a bathroom, do you have a new(ish) hair dryer that may have a teflon heating coil? Were there any bare metal places on the cage or rust spots she/he might have chewed on? Were all toys in good shape? What types of toys were offered? Was any human food offered? Specifically, was anything that could have contained onions or avocado ever offered to the bird? Did the bird have any access to houseplants?
Hope I am able to help a bit at least.