Does using two layers of building paper restrict the drying rate or breathability of the wall in terms of water vapour release?
No, not significantly. The water vapour permeance of two layers of building paper is only about 20% lower than that of one layer and is still well within the requirements of the building code. For example, the building code requires that a breather membrane shall have 170 ng/Pa sec m2 of permeance (2 metric perms). One layer of 30 minute paper achieves about 610 ng/Pa sec m2 and two layers is about 500 ng/Pa sec m2.