Yes, even though obesity is becoming increasingly common, there is still quite a bit of social stigma with obesity, be that direct, indirect or imagined. In all cases the result is often low self confidence and loneliness.
If was of course even worse beforehand, especially when these homes were started many years ago. Because every class had a "fat boy or fat girl" who was more often than not bullied mercilessly, often led by teachers and getting little help from other teachers or parents "children will be children".
But back then at least the most common causes for obesity would more likely have been due to an illness, like diabetes, or psychological issues and while such causes were known, they were certainly not generally acknowledged let alone met with sympathy. So these Christmas mark homes taught dieting, but most importantly they were "support groups", before such things were even invented. And many over the years benefited from a stay as such a home, either personally or because they saw first hand how it helped an unhappy child, sibling or grandchild and that's why the support for these homes has never gone down.
And why there is still a use for them.