Obesity is a mental disability, most often an addiction to a wrong diet containing many addictive ingredients.
The way most people feed themselves is by stuffing enormous amounts of carbs, often a lot of them sugars in their face. Combine those with a little fat and all your body does is store fat and try and balance the glucose content of your blood. The carbs make your gut bacteria generate "happy hormones" that get in your blood, making you hungry and cranky if you don't get your fix, whether your body actually needs food or not.
The symptoms of this addiction are obesity and diabetes type 2. Please treat it as an addiction, not as a phyisical disability. If you do that, for example being taller than 6ft5 should be treated as a disability too and be given all benefits that should come with such a status. If being a size that's outside of what society will cater for is a reason to call people disabled.
Tall people can't help being tall, fat people in over 95% of the cases can help it if they kick the habit. If you treat obesity as a physical disability, you are insulting everyone with a physical disability for which there is no cure.
If it's a mental condition it's one with a strong genetic component.
“Obesity is one of the strongest genetically influenced traits that we have,” says O'Rahilly. Classic twin studies in the 1980s and 1990s, which relied on pairs of identical and fraternal twins, suggest that 40–70% of variation in body size is due to genetic factors.
Mental health can be an issue, I know I put on ~5 kg over two years when dealing with depression, but fat-shaming has always struck me as a failure of theory of mind.
If you're thin it's convenient to assume that it's just a matter of your willpower, you eat healthy because you're disciplined, you eat less because you're responsible. But it's also possible that fatty sugary food is just that much more appealing to other people, that hunger is a much stronger force, that their metabolism is slower so they gain fat much more easily.
I don't dispute for a moment that any of them could lose weight if they tried hard enough. But some people have to try a heck of a lot harder than others.