As far as I have understood in other discussions about the "weekly" backup alternative is that it will be one week old and not the most current if you have made changes within the last 7 days.
I would personally manually click the "Home backup" and then the cpanel will start the process of compressing it (what´s inside the public_html I believe) and download it to my home computer. Then click the databases and aliases/filters, if you have any and they will be downloaded exactly like the home backup.