This article discusses research about pediatric obesity, sleep duration, and electronic devices in the bedroom. Not surprisingly, the more electronic devices (cell phone, TV, video games) were in the bedroom, the more likely the kid would be obese. Also, for each additional hour of sleep, obesity risk was reduced.
It's not clear from the article what contributes to what. I am convinced that screen time affects kids and adult sleep. Getting these devices out of the bedroom can improve sleep quality and duration. I am not convinced that just getting more sleep will reduce childhood obesity. More sleep may improve mood and academic performance, both of which can be negatively affected by insufficient sleep.