Although Amazon started shipping pre-ordered Kindle Paperwhite devices this week, customers who order one today will have to wait a month or more for the e-reader to ship.The backlog for the Kindle Paperwhite e-reader shipments has grown to 4 to 6 weeks, according to the product's listing on Amazon. Once again, Amazon says the delay is "due to popular demand." Amazon unveiled the Kindle Paperwhite device earlier this month as one of its trio of new tablets. The device is Amazon's first self-illuminating e-ink reader. Just last week, the delay was three weeks for new orders.