Looking at the difference in hormone levels between obese people and slender people, we know that fat tissue increases the volume of estrogen in the body. Higher levels of estrogen will decrease the desire for sex. So, if a rapist attacks someone who has a low desire for sex, that victim will be more disgusted with that rape and more likely to file a complaint.
There are a lot of factors that contribute to rapists choosing the victims. Recently, I saw a rather long list of reasons in Pinterest. They interviewed prisoners who were successfully charged with rape. One example that was the first example, which is hard to tell was the most popular reason or not, was that if a female had long hair, a rapist could use that to their advantage.
There are many factors in analyzing the situation of rape, and I’m just focusing on a narrow viewpoint here. I’m not exactly saying that women with higher testosterone want to be raped. But I believe they will be more likely to accept sex and be satisfied with sex. Whereas an obese female may be less likely to have satisfaction with sex and also more likely to turn down sex, thereby disappointing their suitor. Some men take no in different ways.
This is not to say that only women get raped. Men have been victims as well. Obese men are also less likely to enjoy sex and get satisfaction than slender men. So, in a gay relationship, the overweight males will lack lust for their partners, which can cripple a relationship.
So in conclusion, a healthy society will be more likely to have fewer reports of rape than an unhealthy one.