Formulas cannot modify the contents of other fields. They can only read those other fields to pull data into the formula for processing.
That said, what you want isn’t completely out of reach, but it’ll take a bit more setup to pull it off. One option is to use a service like Zapier or Integromat to modify those recurring tasks on a weekly basis. Another is to use the scripting action beta, which could be used to trigger a script to refresh those every week. I’ve got such a setup that refreshes certain things in my planning base every day, and it works great. In my case, the update is done with a script, but you might be able to get it to work with the simpler record update option depending on how you set it up. If you’d like any help with this, drop me a message.