Create a weekly task view?

You can probably do this with the Results Manager add-in from Gyronix: http://gyronix.com/resultmanager.php 

Another option if you sync your tasks with Outlook on your own computer is to use a second map based on Outlook queries. It used to be easier to show individual days of the week with this approach if you used the old Power index add-in which is unfortunately no longer available, but you can still create queries easily at least for today, tomorrow, this week or next seven days and show these as separate branches or sub-branches. You can also establish custom date ranges, though unfortunately these are absolute and not relative.

In theory you could do this within your current project's map, but I suggest that to avoid confusion you create a second dashboard map; this approach also allows you to keep track of tasks from more than one project map. If you have applied Outlook categories to your tasks you can also incorporate these in your query.