Can I set it up so that a form will automatically be e-mailed to a group of e-mail recipients weekly?

To my understanding, you are looking for a way to send the link to your form via email. However, you would like to send it automatically to multiple recipients weekly.

Although there is a way to send the URL of the form via email — How-to-Send-a-Form-via-Email within JotForm, there is no way it can be done automatically every week.

Perhaps you can try the following third-party apps:

https://zapier.com/apps/gmail/integrations/schedule/2811/send-a-weekly-email-with-gmail

https://www.boomeranggmail.com/l/recurring-email.html