Is being called curvy a nice way of saying fat?

It did not used to be. But that alas has changed. Up until the early 2000s or so it referred to someone who was both not obese nor sylph-like but rather curvaceous, like Sophia Loren in the the late 1950s and early 1960s:

Now “curvy” is a term mostly used by massively obese women to feel better about themselves. And that is certainly not an improvement.