Mangakas have no idea how weight works + insane asian standards of what normal, thin and chubby/fat looks like.
I see nothing wrong with the way this story was done in terms of the behavior of the two women. I have known MANY perfectly healthy-looking women (and some men as well) who have insisted that they need to diet because they were getting "fat" over the years who behaved precisely the way Akari does: ordering smaller portions while looking longingly at the food the really WISH they had ordered. It doesn't mean they ARE overweight. It has to do with body image and how their clothes fit. If you add in eating disorder issues (and there are several people on both sides of our family with those, unfortunately) these behaviors amplify and also become warning signs of something potentially dangerous.
I'm curious as to why Akari first assumed cheating of all things (Maybe a translation deal?) because Shiho doesn't seem like the type to do that nor does Akari seem the type to assume that.
To be fair, this is likely the first time Akari's even seen Shiho interact with another person without being present. Just goes to show how much they're together.
^^ I suspect this could be part of it. When Akari is approaching the two of them they are standing VERY close together. Far closer than Shiho is likely to allow someone who she is not very close to into her personal space. In addition, Shiho's sister is very obviously enjoying the conversation, considering how broad her smile is. Shiho is also MEETING HER EYES, which I'm guessing is not something she tends to do with others. So it's not surprising that she felt jealous and put on a little dominance display.