A little more complicated than that. Fat suits are common in Oblivion and Fallout 3, but it's the clothing that makes the body fat. Animation skeletons are not updated to account for the extra body size. Changing clothing can break the effect unless the new clothing matches the body shape.
You can use animation bone scaling to simulate fat people and then the clothing will change to suit, but this causes stretching of textures on the models and often looks weird.
Doing it properly requires the ability to assign individual skeletons and body models (or at least different animations) and clothing that adapts properly.
No. You are making it too complicated.
This is how it works:
You import the regular mesh you want to make "fat" into a 3D program, and either using a lattice, sculpting, or simply connected grab and pull, you make the mesh a fatter waistline, love handles, bigger thighs, etc. Unless you plan on making the mesh morbidly obese, the textures will not distort that much. Textures with patterns usually show more distortion, but you could easy just paint over the .dds a solid texture, no need to re-skin.
Once your body and armor/clothing meshes are done, you create new a race or races, and assign your "fat" body mesh to it. Then you create your fat clothes and armors and put them on the NPCs you want to be fat. Voila!