You want reassurance that she’s a “real” friend…and the only way to prove that is for you to see a picture (which may not even be of her)?
You may have met people in real life…whom you’ve had face-to-face interactions with…whom you consider “friends”…and they turn out to be insincere. Did seeing what they look like guarantee their sincerity?
You claim that you don’t have a romantic interest her and this is based upon her telling you that she’s fat and unattractive. So, it’s just based upon HER words/description of what she looks like. Now…what if she’s being her own worst critic…and is not even half as bad as she has made herself out to be?
Also, I wonder if she herself only sees you as just a friend…or something a wee bit more than that?