On a weekly plan your service renews every 7 days.
The Next Due Date shown on your service is the date your current paid period ends. It is the date the next payment is due — not a date you are being charged on repeatedly in the meantime. An invoice is issued shortly before that date so you have time to pay it.
You are only ever charged once per period. If you have paid for the current week, nothing further is taken until the next due date arrives.
If you do not want the service to renew, request a cancellation with the End of Billing Period option. No further invoices are generated after that, and the server stays usable until the due date.
If you need help with this, please submit a ticket.