It is normal to be able to pull one's skin away and have it rebound. This is what your skin is doing. If the photos don't show the true nature of the problem, consult a Board Certified Plastic Surgeon or Dermatologist for a skin biopsy to see if your skin elastin and collagen fibers are abnormal.
The photograph is limited but I don't see any specific problems. When you generate facial expression the skin will banding kind. When the expression is relaxed your skin is recovering nicely.
It is very difficult to give an answer with these photographs. I would suggest consulting with a surgeon for a proper diagnosis to see if you have any abnormalities with your skin. Best regards, Michael V. Elam, M.D.
It's difficult to evaluate your situation with those photos but you do not appear to have a problem with fat. There are syndromes which have abnormal stretching of the skin as a feature but you don't really look like that either. You should discuss your concerns with an experienced plastic surgeon and don't be offended if they suggest a referral to a psychologist. If you're spending more than a couple of minutes a day studying your mouth and smile, DO NOT have surgery until you discuss this with a psychologist.