Since about 10 years ago, I have followed, on and off, what is called Fatosphere: the blogosphere of body positive bloggers. Many of them are also part of HAES: Health At Every Size, the approach that you can engage in. healthy behaviors regardless of size and that weight loss should not be a goal of healthy behaviors.

Many in this community, fat people themselves, reclaim the use of the term "fat" (and big would be OK, too), as an objective term. They actually do not like the term "obese" which makes it appear a clinical disease. They would rather be called, objectively, fat. Check out the blog Dances with Fat: that blogger, being very big, has done marathons. It would blow your mind.

So no, it is not the case that no one likes to be referred as objective terms fat or big.

I have been called, very nicely by caring people, a big woman. I do not object to that. How would you call me if I am objectively big?!