Although the word looks very English, it is not. As it turns out, its origin has nothing to do with the word house, but can be traced back to the Anglo-Norman word pentis (defined in AND#1 as ‘pentice’ and ‘small building’). This word, pentis, is an aphetic form (i.e. a word that loses its prefix, a process which is not uncommon in Anglo-Norman) of apentiz (also listed, separately, in the AND as ‘penthouse’ or ‘outbuilding’).
En Jèrriais j'avons appotis ou appentis; eune appentie est eune grôsse femme!
In Jèrriais a lean-to is appotis or appentis; appentie means a fat woman!