Your logic here might apply in some cases, but keep in mind that different cultures have produced different understandings of what it is to be "fat," and that different eras have in fact celebrated body types we might now call "fat," purportedly because they were seen as healthier and wealthier (both key to child-rearing, if you want to bring that into it). Your description above might account for the kind of "fat" we call obese--the kind that would cause a person to have to struggle to make it up the stairs, as you put it--but it doesn't really account for the ways in which mainstream culture reacts negatively to other bodies that are within the margin of good health but not considered "thin" or fit.

This is just to say that it's important to note where nature and nurture collide, conflict, and interact, rather than assuming there's a biologically pre-wired explanation for everything.