Yeah, I live in Japan. I can say there are very few obese people in Japan. There are one of two options that will happen:
The first, which is true 99.57% of the time. She will be ignored. People here ignore everyone, regularly. Japanese ignore Japanese. There is a term in Japanese to describe this social indifference and intense inward ("me") focus. They do not make eye contact. If you are not sure what I am talking about, when you get off then plane and think, what's wrong with everyone... remember what I have written here. That is what you are feeling all around you.
Foreigners here (especially Tokyo / cities) are ignored even more because Japanese are deathly scared of speaking English and even more scared of failure (for anything) so they simply live their lives in rigid, predictable, linear communication patterns. An encounter with a foreigner in English is in the "does not compute" territory and in the realm of ambiguity, which Japanese people don't do. They don't do ambiguous situations at all. They shut down and brain-fry (internally) if faced with ambiguity. Culturally they are brought up to be xenophobic with really strong in-group (Japanese), Out-group (the world) thinking. This means you will also be ignored HARD as will your entire family. They don't do this on purpose, it is passed on, like religion is wrongly passed on to babies/children by their parents. They simply have no say in the matter of "Gaijin" (foreign people) and they carry many false stereotypes that persist unchecked from generation to generation because that is what they know as truth.
So, she should be totally ok everywhere in Japan. No one cares about her or you. People just care about themselves here. Too many examples to list. Been here 8 years.
The other extremely rare cases are explicit, overt racism, which has unfortunately happened to me 3-4 times. This will not happen to you. The chances are very very low.
In general, no one shames people here in public. If they can't even notice others AT ALL and cannot speak to strangers, which they don't do at all, how can they possibly shame your daughter? think about it. In schools or perhaps other small regular settings, with only Japanese people, definitely shaming occurs. This is a universal trait of humanity. FYI
Everything you understand about Japan is wrong. I hope some others have posted truths here as well.