When my DS was four, he asked a cashier on a till "Why are you so fat?" I wanted to disappear through the floor. I said nothing for about five seconds while horror and embarrassment flooded through me, and then I lamely said, "I'm so, so sorry. That was so rude! I'll speak to him about it later, but I'm really sorry." The guy was lovely about it but to this day, years later, I feel bad about it. 
I had a long chat with my DS. He still went on to say it about three to four times at various points in his childhood. AS he got older, I became more scolding than educating, as I felt he was old enough to know better. Fortunately, that did the trick.
What I mean to say is that the children don't always reflect the attitudes of the parents. I've never called anyone fat - either to their face or about them - around my children. Even when my children aren't around, I wouldn't use the word fat, either - it seems so loaded with negative connotations. I would either use the clinical term - obese, or be euphemistic - she's a well-built lady for example. My best friend is obese so I understand how sensitive this can be.
However, that doesn't mean you have to let it pass. Next time they say something, look at them directly in the eye and say, "Do you know that using the word 'fat' is really unkind? It's very hurtful. If you call me that again, I will feel that you want to hurt me on purpose, and i'm sure you don't because you're a lovely little girl/boy who I'm sure would never be so spiteful."