My Brilliant Life
두근두근 내 인생 (original)
A couple of teenagers have a son who suffers from progeria, a rare genetic disorder which makes one age exponentially faster than normal. 16 years later, the child has the body of an 80 year old in the final days of his life writing a book about his parents' love story.
Starring Gang Dong-won, Song Hye-kyo, Jo Sung-mok, Baek Il-seob, Heo Joon-seok, Kim So-jin, Cha Eun-woo, Chae Seo-jin, Lee Sung-min, Kim Kap-soo
Watch "My Brilliant Life" on Tubi TV released in 2014. It's a drama and family movie, and has a rating of 7.2 out of 10 from Imdb which is usually fine for this kind of movie, and is currently available to watch for free.