Bradshaw of the Future tells us: 'The Proto-Indo-European root *peiH- "to be fat, swell" in the extended o-grade form *poid- became in Proto-Germanic *faitaz "fat". This became Old English fæt and then English fat. In Proto-Celtic, the extended form *pī-wer- "fat, fertile" became *f–weryon- "earth, soil".'
Is soil 'fat'? Is the rotund, hippy Earth fat? Of course, of course.