The idea of robots taking over everything is not a practical idea. Why not? Because robot operations don't pay people. So, who can afford to buy the products robots make? Certainly not people. And the robots don't need the products. So, the company fails.
The way this will work is when the robots can manufacture the products cheaply enough that people can afford them. People will have jobs that the robots will not take over - at least, not for a long time. These jobs will be low-paying jobs. So, the robot factories will need to make their products extremely cheaply, just so that people can afford them.
Ultimately, the products will cost nothing, because the robots will have taken over all the jobs, and the only way the people can get the products is to get them for free. This is not really a practical idea, because people will always invent new jobs that the robots will not have the ability to do until somebody invents robots to do the new jobs. There might be some kinds of jobs that robots will never be applied to, like inter-human friendship and enjoyment - which might become a job in absence of all else.
Anybody who wants to extend AI-robot operation, should start to make the robots to have jobs among themselves, so that when humans fail to buy, they will be producing some items that other robots will buy. This will maintain profits, and keep the robot companies going.
As for obese people, not everyone remains inactive. There are loads of people, who, if they didn't have to work on a job, would travel the country on bicycle. AI-robots might actually be the cause of the reduction of obesity.