If more than one bird is expieriencing this then it definitly isn’t a stroke, balance issues is a common symptom of metal poisoning, but it is strange that they’ve gained weight.
do they just look like they’ve gained weight or have you weighed them on a scale and seen that they’ve gained weight?
An x-ray will show bits of metal in their system if they swallowed it, a blood test can determine if it’s zinc or lead. Chewing on galvanized metal or paint can poison them, if that’s the case an x-ray would show nothing.
Other possibilites that cause incordination are vitamin deficiencies, feed contaminated with aflatoxins, kidney or liver failure, or certain diseases like avian chlamydiosis.
Chlamydiosis can be treated with antibiotics, aflatoxin exposure requires supportive care, boosting the amount of antioxidants they eat and giving milk thistle.
I’m sorry your poor geese are sick, I have a gander that has been fighting liver issues for a long time now, I wish I knew what did this to him so I could prevent it from happening to my other birds, but like many bird parents sometimes we never know and all we can do is guess.
I hope you can figure out what this is making your geese sick and I really hope it’s treatable. I’ll keep your flock in my prayers.
This is a sight that I use to look up different health issues, it’s tailored to ducks but most of it is true for geese too.
http://www.duckdvm.com/view/symptoms.php