As a fat fud myself, I've never had a problem. I've appendix carried almost exclusively most of my life, and have done so even with a 6-inch Dan Wesson revolver. The key is how you carry yourself while carrying. I've open carried, yet most people haven't been aware of the fact, simply because of how I keep my arm tucked to cover the weapon.
Breaking up the outline is key, which is a lot easier for us fat guys than skinny guys. Use an inside-the-waistband type of holster. Wear loose untucked shirts. If someone is going to be LOOKING for CCW, you won't fool anyone. But to 95% of the the unobserving sheep will have no idea. In cold weather like now, its no challenge at all. Wear a thin or thick jacket and everything is pretty easy to conceal.