Hey there!
I think that if you want to talk about weight, you mustn't forget some important things. The first is food. It's not only quantity that's important, but quality, too.
We all know that we, today, eat too much junk food. But we also happen to eat much more vegetables and fruits. Just think about it: it's true that people in old times ate less then we do, but maybe their diet wasn't balanced, either.
Some kind of food, like fruit, was almost impossible to transport or preserve for a long time. Our grand-parents were given oranges and apples as Christmas presents, and OTMAA may have never seen bananas or mangos in all their lives. So if they ate only breads and meats, it's no wonder it must have affected the way their figures looked.
I don't think Nastia was really "fat". She was chubby, it's true, but she wasn't that overweight. She would have outgrown it, just like Maria had.
The second important thing you musn't forget is the effect that puberty have on girls. One of them is that they put on fat, it's a natural condition for a young boby whose preparing itself to bear children. I think it takes some girls time adjusting to the changes. That's why teen's faces are more chubby than kids. Ten-years-old are often built all in lines. It's the case of much less 15-years-old.
Oh, and by the way, don't forget that girls hit puberty earlier today than around 1900. It's another effect of an overall better nutrition plan on the human kind. So I would be surprised if Nastia really became a young lady at age 15 or 16 and got a little fatter because of that.

But of course, I'm only talking about things in general, here. For example, I must be at least 5'5'', and I haven't really put any weight on since I was 14.
It's just ideas, so I'm sorry if I sound too much like a little annoying one-who-knows-everything.

It just seemed a good idea to share.