There is a psychological term that might work for you, if the worry is truly constant. Body dysmorphic disorder (sometimes body dysmorphia)
is a mental disorder in which you can't stop thinking about one or
more perceived defects or flaws in your appearance . . . . When you
have body dysmorphic disorder, you intensely obsess over your
appearance and body image, repeatedly checking the mirror, grooming or
seeking reassurance, sometimes for many hours each day.
(From the Mayo Clinic's Patient Care & Health Information)
Note that the perceived flaw can be anything, including obvious things like weight but also things like obsessing about a particular body part, and that it is usually unnoticeable to other people. A commonly related disorder is anorexia, whose sufferers may believe that they look fat even as they starve to death. (See, e.g., this article.)
This is distinct from traditional notions of vanity, as the obsession with appearance generally does not arise from pleasure or pride in that appearance. Narcissus, for example, fell in love with his own reflection (Wikipedia). A sufferer of body dysmorphia, on the other hand, may also spend an inordinate amount of time looking at his or her reflection, but would be distressed by what he or she saw there.