I'm an American man with a 38 inch waist. My doctor says I fit the definition of obese. I have spent a total of 12 months in Japan, split among 10 long trips. I think that Japanese people are used to seeing large foreign tourists. I have never felt singled out in any way in Japan because of my weight. If anything, people have been kind, silently adjusting their chairs so I could more easily navigate the crowded breakfast room at the hotel. Japanese people are polite and want to make a good impression on foreigners. Of course, I don't understand Japanese, so if people were talking about me I wouldn't have understood it. I have never gone to any onsen, which might be a high-risk area for comments.
I have been singled out in Japan for looking vaguely middle eastern. Two photography hobbyists politely asked to photograph me. Police stopped me at the Narita airport train station and asked to see my passport. And my luggage has been subjected to special inspections twice at airports.