It's a long while since I looked at this, but IIRC:
Crew input ZFW and ZFCG via the MCDU.
FM transmits this to the FMCG, which calulates a gross weight.
Incidently, GW and CG on the EWD are driven by the FCMC
Gross weight gives the CG target, which is used to calculate how much fuel to transfer aft.
FM acts as an independant monitor, and if it detects CG going to far aft, it tells the FCMC to transfer fwd.
Of course, the details are all pretty dependant on software levels and 200/300 / 340-600 etc.