Actually, come to think of it, it should be possible to get a ballpark figure without working out the equations in detail. Take the example given in my link of a fat molecule with 58 carbons, 112 hydrogens, and 6 oxygens. Since carbon has an approximate atomic weight of 12, hydrogen 1, and oxygen 16, carbon makes up about 77% by weight of the fat molecule.
If the fat is completely catabolized, all of the carbon will be removed from the body in the form of carbon dioxide. Therefore out of every pound of fat lost, a minimum of 77% by weight is exhaled away. Most of the oxygen in the carbon dioxide comes from the air. Offhand, I don’t recall whether the relatively small amount of oxygen in the fat - 10% of the total weight - ends up in the carbon dioxide or the water. So, very approximately, between 77 and 87% of every pound of fat lost is removed as carbon dioxide, and the rest as water. (Note that the carbon dioxide and water excreted together will actually weigh more than a pound, since some of their weight will come from atmospheric oxygen.)