It's definitely NOT good for a young, growing horse to be fat. It's actually preferable for them to be on the lean side. Carrying all that extra weight is adding stress on their joints.
It looks like he lands toe first in the video sometimes? Have you noticed that? I might be a bit delirious from sickness and lack of sleep LOL. He seems overall ouchy throughout the entire video, not wanting to put too much pressure on his fronts, dragging his hinds(though he does that in the clicker lunging video, too.) He could have some heel pain, abscesses forming, or could be suffering from the beginning stages of laminitis. Can't wait to see what your vet says.