To me the fat dog makes sense. 2 cups no exercise trim the food back a Lil at a time down to 1 cup a day. My concern would be the thin dog receiving that much food with no exercise and staying thin.
I can let the other dog (1/2 BMC, 1/2 Walker) run around and she wont run off, if I let my Mt. Cur (the fat one) he's gone.