Back when I was younger and political correctness was in full swing there was a joke about a woman who got her purse snatched, went to the police, described the culprit as African American (the PC word) and got the disdainful response "And how do you presume to know he was an American?"
Political correctness is just insane. I've seen examples of people calling people from Africa, who live in Africa, African American. Nelson Mandela is not African American. Nelson Mandela is African. Period. South African if you want to be specific. White Africans are just that, or Africans of European descent. There is no point in calling a black African an African of African descent. Likewise there are a lot of dark-skinned people in the United States who are not African Americans. One of my best friends in high school's family came from Haiti. They were not African American. Haitian American, sure, but not African.
Likewise fat people are fat. There's often a moral judgment attached to that, but there doesn't have to be. There doesn't not have to be either. Maybe the victim of this hit and run is really mad at the fat woman who hit her. Maybe she wants to insult the woman by calling her fat. Calling someone fat rarely kills them. It can't even get them to put down that danish. Trust me, I know. The job of the police is to catch people who commit crimes. Hitting someone with your car and driving off is a crime, and a serious one. People die every year from being hit by cars, and specifically from being hit by the cars of people too self-involved to call medical attention to someone after they hit them.
Calling someone fat is not a crime, and not really within the purview of the police. It's none of their business.
Racism, ageism, sizeism, and all the rest of the isms are problems in this country and society at large. Fighting them is a good thing. The way you fight them is by speaking loudly and providing examples of why they're preposterous. You don't fight them by legislating language and attempting thought control. There are a lot of non-racist people who use the world "black" to describe other people. There are plenty of racists who use "African American." The same holds true with fat and "person of size." It's actions and attitudes that count. Sticks and stones can break your bones, being called fat? Well, like I said, it won't even get you to put down that danish.