Troubleshooting high network traffic between primary and secondary replicas
If you have high outbound network activity on the primary server, and high inbound network activity on the secondary server, it is very likely that there is an increase in logged (write) actions in the availability group databases during this period on Saturdays.  these are getting synchronized to the secondary, resulting in a lot of network activity.

One option for catching this would be to log sp_WhoIsActive to a table during this time period.  You can come back and review these logs to see what queries were running to produce all of this extra AG sync activity.

You mentioned you ruled out scheduled jobs, but this sounds suspiciously like a maintenance activity - rebuilding indexes is something often done on weekends, and it produces tons of traffic in AGs.