Sure.  Just follow the steps below:

1.  To set up a weekly status report (this will need to be done individually per campaign that you want a report)  log in to the Campaign Manager
2.  Open the active campaign
3.  When you are looking at the campaign there is a "reporting" button in the upper section of the screen, click it and chose "Report Subscribers"
4. The next screen will have a drop down for "Manage Campaign Subscriptions", click that and chose "Weekly Status Report"
5. Another window will load, showing everyone who is able to have this report sent to them. Single-click the person's name to highlight, then click ">>" to add them as a Current Subscriber
6. Once that person is added you can click close

Note:  The reports can only be run on currently running campaigns. The report gets e-mailed at roughly 8am Eastern time every Monday until the campaign expires.