What are some polite ways to refer to fat people?

Refer to them by their names and by things about them which have nothing whatever to do with their being fat, such as achievements and awards and positive characteristics. 

Why do you need to label anyone?  Just call them by name, or if you don't know it... how about Sir, Miss or Ma'am.

Instead of using fat just say over weight

So, I'm considered... round. I hate that I'm being classed into a "them" category. The offensive ones are: Large, Wide Load, Fatso, Porker, Thunder Thighs, Lazy A**, Portly, Rotund, Huge, Whale, Cow, Big Boned, Chunky, Fatties and Fat. The medical terms are acceptable because they are professional: Obese and Overweight however unless you're a medical professional you ought not use them. The ideas of embracing size such as Curvy, Goddess, Plus Sized, Thick can go out the window. I don't want to be a bigger gal (preferred term) but my genetics say otherwise.

If you are a medical doctor, you should have learned the medical terminology for unhealthy weight in med school.

If you are not a doctor, there is no need and no polite way for you to talk about other people's body fat.

plus size I guess

Chunky, comfortably mature in size, rubenesque...

If have to use it, you could use ' obese or obesity '.

"Rubenesque" - you'll understand the significance if you know how Rubens painted people, especially females!

Try not to refer to a person';s weight at
all----If
 you must speak of the person as being a large person the listener will know what you mean