The Oxford English Dictionary defines obese as "Very fat or fleshy; extremely overweight" Check your definition. What does being impoverished have to do with anything? Why is it that people think that hypothetical situations are valid arguments? They could very well be "impoverished" and still be fat.
There is a reason that it's called being overweight. For weight there is a spectrum that people can be within and still be considered the ideal weight. This woman and others like her are beyond this spectrum. Is that better for you? By the way impoverished means reduced to poverty, poverty stricken, really it has to do with wealth not weight. Maybe you meant malnourished. Either way, it's not healthy and calling someone fluffy isn't the way to help people. You are giving them false comfort.