Exterior Door Width is Shorter than Jamb
Unless I am mis-understanding what you are calling the door jamb.  The door jamb is the vertical strip nailed to the door casing to provide the door stop when closing.  It would be easy to replace the jamb with a thicker piece one (about 3/8&quot; thicker).  I would not shim the jamb.
Weatherstrip is normally added on the exterior side of the door.