The barycenter is a balancing point. If you were trying to balance two objects on the ends of a see-saw, if you move one object farther away, the balance point has to move toward it (you're actually balancing moments of inertia, which are functions of radial distance.)
If your gravitating objects are in an orbit, they also have angular momentum and moments of inertia.
If your gravitating objects are in an orbit, they also have angular momentum and moments of inertia.