No it is not possible. Humans are heterotrophic organisms, which means that we use organic molecules (i.e., food) as a source of nutrients and energy. We use the nutrients to add mass to our bodies. These nutrients are the familiar carbohydrates, proteins, lipids (fats), etc... During digestion food is broken down into simpler organic nutrient molecules that are then used to make our body tissues.
So even if we only used food for nutrients we could not gain more weight than the food we consume but note that the food is also used for energy. This means that some of the mass of the food that we eat is not used to add mass to the body but is "burned" as metabolic fuel. The mass of the food used for energy is expelled from the body as waste in the $CO_2$ that we exhale and in the metabolic waste in the urine.
The carbon in the air is mainly $CO_2$, which is an inorganic molecule. Only autotrophic organisms like plants can use inorganic molecules as a source of nutrients. Since inorganic molecules usually contain less potential energy than organic molecules autotrophic organisms need a different source of energy. Plants use sunlight.
Finally, fat contains about 9 Calories per gram whereas a Big Mac has about 2.4 Calories per gram so fat has almost 4 times the energy of a Big Mac.
(Calories are the amount of heat that is released if all of the energy in the organic molecules is released so it is an estimate of how much energy the body can get from food)