Do fat people not like being told they are fat?
Intention is important. Other than a medical doctor, why would anyone feel the need or entitlement to point out that a person is fat?
Nobody likes to feel criticized. Our society is strongly biased about obesity and perceives it as a defect or a personal fault. An epidemic that needs to be eradicated. Some people seem to feel that it's okay to actually hate someone for being overweight. To that end, it's become hugely insulting to point out that a person is fat. It reeks of judgement, criticism, meanness and even an offense in line with a racial slur.
Also, it's no one's business. Even without malicious intent, there's no "polite" way, or reason for that matter, to tell someone they're fat.
We all have things about ourselves we'd like to change. When it's a character flaw we can try to shelter it from the world, keep it hidden and safe. Or, at least less obvious. Body weight isn't one of them. We wear our relationship to our body right out in the open. It's extremely personal, but there's no way to keep it discretely to ourselves.
People who are self-conscious about being overweight feel it everyday. Why do feel the need to "inform" them?