Currently, syncing weight to Zwift from Fitbit platform only works if weight is recorded by Fitbit Aria scale.
However, there are other scales that can record weight data to Fitbit, such as RENPHO. Strava syncs this weight data without issues, but for whatever reason, Zwift decided not to. This decision makes no sense to me, but that is confirmed by Zwift support as working this way intentionally.
Zwift, please remove unnecessary obstacles to having up to date and accurate weight data.