People who are chronically sleep deprived have been found to suffer from obesity, type 2 diabetes, and other chronic diseases.
… and in a short time frame
While otherwise healthy people typically lose their weight after just 5 nights of getting just 5 hours of sleep, 5 consecutive nights of sleeping just 5 hours per night has been found to promote weight gain. I can tell you about that at here.
Unfortunately, people usually go to see the doctor for sleep because many prescription drugs have a long list of side effects. You can learn more about prescription sleep medications on the FDA's website.