Why is fat sticking out of corner of my left eye? (photos)

Thank you for sharing your case and photos.  This is a common condition where the fat that is normally behind the eye starts to stick out.  It can be removed during a simple outpatient surgery.  Schedule a consultation with a board certified oculoplastic surgeon to discuss your condition and make sure your eyes are otherwise healthy.  Good luck!

Your photos are consistent with a common condition that comes with aging -- especially in people who have shallow orbits and lax eyelids. There is some orbital fat that can bulge forward and be noticed as your photos seem to show. But only during a complete examination with an expert can a definite diagnosis and treatment plan be made. You need an in-person consultation with a board-certified, fellowship-trained Oculofacial Plastic Surgeon with extensive experience in orbital and  eyelid surgery.  Many patients travel great distances to see me for this sort of expertise. You must avoid any doctors that perform orbital or eyelid surgery part time, they cannot help you. Bulging orbital fat is not a medically covered procedure -- it is considered cosmetic surgery by insurance companies. I have performed this procedure many times with beautiful results.
Best of luck to you. 
Damon B. Chandler, MD
Harvard-Penn Trained Oculofacial Plastic Surgeon