As far as i'm aware , and read here on forums , technically you only need to complete ALL Weeklys once ( the 1st tme ) in order to "unlock" initial Rank progression.
After that, it's just more for guidance "homework" type list , to keep things a bit more structured or interesting or whatever. ( plus bonus merits for completing them )
Yes, that is the expectation...but its still only week two so...we won't know for certain that is the actual case until after 7AM UTC Thursday next week.