Such changes are called germ-line mutations because they occur in a cell used in reproduction (germ cell), giving the change a chance to become more numerous over time. If the mutation has a deleterious affect on the phenotype of the offspring, the mutation is referred to as a genetic disorder. Alternately, if the mutation has a positive affect on the fitness of the offspring, it is called an adaptation. [Nature]
I'm assuming you mean "mutation that gets passed down". Whether a mutation is a disorder or an adaptation takes generations to determine, so we may not know the identity of the individual. Furthermore, what was once a disorder may become adaptive in a different environment and vice versa. In general, I suppose if it was adaptive, they might be called "ancestor" :)
More broadly, and outside of germ-line mutations (meaning it's not passed down to offspring), everyone has cells with mutations. The person doesn't have the mutation per se, but a cell or cluster of cells do, so identifying them by that mutation doesn't make a lot of sense. If it's bad, your body either kills it or it kills you (e.g. cancer). If it's good, it likely doesn't change anything significantly.
Have you ever heard the phrase "You can't reason someone out of an opinion that they didn't reason themselves into"? If they're objectively not fat, than what they're really saying is they feel like they're fat, not they they think that they're fat. That can be for a whole host of reasons, but arguing facts with them won't help. Far better to have discussions with them about why they feel that way and why they're focused on it. Ultimately it's an issue they have to resolve themselves and not something you can convince them of.