When a customer orders from a website on Fridays and pays for overnight shipping, I´ve noticed that a lot of them expect to have the item in their hands on Saturday.
Unless you offer (and the customer chooses) one of FedEx or UPS premium delivery services, there will not be deliveries on weekends – even with FedEX overnight or UPS Red. And if the weekend is a long one (like Memorial Day weekend just passed), a Friday overnight order will not arrive until Tuesday.
I´ve found it pretty good practice to let the customer know this before shipping — a simple form email will work. That way they won´t be expecting a Saturday delivery that never arrives. While many customers are savvy enough to know this, some aren´t and you may save yourself a possible complaint later on.