How to schedule PostgreSQL replication?
You can use pg_basebackup to take a copy of the PostgreSQL database over the replication protocol. It copies the whole DB though, it isn't incremental. You'll want to use the --xlog-method=stream argument unless you have a shared WAL archive set up.

Streaming replication isn't really well suited to the purpose you describe. You can set it to have replication lag, but it's more minutes or hours rather than days, as the amount of WAL you have to retain on the master or in an archive to get days of replication lag is huge. It's also fixed, not schedulable.

You could achieve what you describe with lots of WAL archiving plus a custom-created recovery.conf for each backup, but it'll be fiddly at best.

The thing you need to realise is that by (say) Friday, the master no longer has any record of the state it was in on Monday. It can't update last Friday's snapshot to this Friday because it no longer knows what state it was in on intermediate days like last Monday ... or last Friday. It doesn't know what state the old replica is in, nor how to get it from there to where it is now.

You can tell it to remember that much state by archiving WAL segments, but you need an immense amount of disk space for that and it's very inefficient to catch the backup up from WAL if your DB is busy.

I'd recommend just using pg_basebackup and/or pg_dump on a schedule.