How important is maintaining a good weight through a weight loss program?

Not sure. Im not sure i understand your question . The goal is weight loss. Depending on the program and as long as you are losing fat not muscle you should be fine !
Helps protect muscle. Will alter body composition - good weight balance helps preserve essential muscle mass - if done without proper supervision can mean damage to heart and gut, and loss of muscle with altered body composition. People will have aged look and emaciated body.