Stims are hard to stop and in most cases harmless. They do serve a purpose to an ASD child and as long as they are not hurting themselves it is ok. I know it looks weird in public and draws attention so you can try to redirect the child but with us it works for a few minutes and they are back to it again.

I've heard about low muscle tone in kids with autism but we don't have that problem. There is a benefit to all the jumping. My 4 year-old daughter has some real muscle on her legs. She to be unable to catch anything but now she can so perhaps we can channel her energy into some activities.

For us hand-flapping is symptom of yeast and we treat for that. Don't have hand flapping at the moment as we have this under control at the moment.

For jumping, perhaps get a small trampoline, and try to teach jumping there as the more appropriate behaviour if there is some sensory need instead of stairs, couch, bed, etc. We haven't done that yet.

Stimming helps them regulate how they feel. I wouldn't try to stop the behavior but maybe help them do it it private

I can only imagine to You or I it would seem weird but for them it's normal and we want our children to feel normal it isn't hurting anything and like the previous post stated the child is doing it for a reason if you've ever heard of Carly she explains how other noises and sounds and lights around her are over stimulating for her so she drowns them out By humming or like my son does by rocking. Best of luck and I think you should just let him do it because trying to make him do something else instead may be like hitting a wall and just a waste of time