I think what he said was inappropriate and done purposely. I don’t think that for a second that he would be asking if her parents were fat if she was an overweight white woman from the States.
The best possible explanation for what else he might have meant that we can come up with here is "Americans are fat, so if you are from somewhere else, your family must be skinny".
That's the BEST we got, and feels like quite a reach, I dunno how a perfect stranger is supposed to get to that reasoning, and the first thing
we think of is some starving African joke.
Seems to reason a black woman might get there too.
Is it offensive? No idea, we dunno what he meant, but a better question is,
would it be reasonable/understandable if this woman was offended? I think yes.