It is possible to send the same survey to a list multiple times. You'll just need to schedule each weekly distribution individually. In other words, there's no option that allows you to schedule a distribution automatically on a recurring basis, like a repeating calendar appointment, for instance.

I set it up using workflow in Qualtrics

If you are in the messages tab go to the bottom of the window and turn "on" the Participant reminder rules and then set the days and how many times .