It will do when your ankles and knees give up !! 
You'll find the vast majority of people who're sat in a doc's surgery with knee and ankle problems are the ones who're overweight.
And it's not purely a mechanical problem either; overweight people tend to suffer with arthritis more - not just in their weight bearing joints - but in places like their fingers.
There's evidence to show that the body likes impact (the kind you get from running). It increases bone density and encourages the growth of new cartilage.
So there!