My son is wanting to exercise with me but he's only 5, I'm wondering what's okay...

[Chad B]

...for him to do? I like to exercise. Mostly just running outside and on the treadmill, but lately my sons been wanting to exercise with me. He asked if he could go on my run with me, so I let him, I just shortened it and walked more than ran. I also have a weight room in my basement and he likes to be with me when I work out, he ask if he can walk on the treadmill, and I haven't seen any harm in it, so I've been letting him. People are telling me it can cause appearance issues in young children, is this true? Is it okay for him to do limited exercise with me? Pleaes help