Does a depressed fracture of the zygomatic arch need to be repaired if there is no pain or noticeable cosmetic change?

Neither his cheek nor nasal fracture have to be treated. Six weeks is a long delay for closed reduction of either injury. There is a reasonable chance that any movement in the nasal or cheek bone will be short-lived without actually creating cuts (osteotomies) in the fracture (now healed) bones. Regardless of the timing the indications to fix the cheek bone fracture would be difficulty opening the jaw, discomfort or cosmetic deformity. It does not sound like any of these are occurring at this time. There is a small risk that as your son heals more fully swelling will resolve and unmask a deformity of the broken cheek bone.Stephen Weber MD, FACSDenver Facial Plastic Surgeon 

At 6 weeks  most bones are fairly well healed into place and will be very difficult to re-set them without osteotomies. As long as the zygomatic arch isn't creating a functional or cosmetic issues, it is best to leave it alone.The nasal fracture can be  repaired at any time, but will require osteotomies and shaving the hump down and straightening the tip.