If you need to purchase web hosting and want to pay by the weeks instead of by the month. You will need to contact your web hosting provider and work out an arrangement with them. Most small web hosting outfits will make reasonable accommodations if you have a reason why you want to pay by the week instead of normal terms.
If you attempt to pay a large web hosting firm by the weeks. The chance of getting any agreement in place is almost non-existent with the exception that the transaction involves 4-5 figures ($x,xxx to $xx,xxx) in payments.