This would be an interesting study but on an individual basis there are too many factors to consider. First off, everyone has their own idea of what's a comfortable amount of personal space, whatever their size.
Also I'd imagine it would depend upon when someone got fat and how much weight they've gained. Someone who grew up fat might not be as aware of the dimensions of their body βΒ or the opposite, where they're overly self-conscious of how much space they take up.