Currently, policies in the USA and UK favor giving RhIg to women who type as weak D.
In Canada, the Society of Obstetrics and Gyneacology recommends not giving RhIg to women who type as weak D BUT in some locations, weak D women do indeed receive RhIg in pregnancy.
Many other countries also recommend not giving RhIg to women who type as weak D but policies again vary even within countries.
Summary: Because policies vary internationally and change over time AND because the availability of molecular testing to differentiate weak and partial D Rh types will evolve, recommending a specific protocol for RhIg administration and weak D status is difficult.
Consult SOPs and policies in your transfusion services manual for the situation in your locale.