It's not so much the bank, per se, it's the Fed.
When you transfer money into an account, it does NOT go to the bank, it goes to the Federal Reserve clearing house (in Tennessee), then it goes from the Fed to the receiving bank. All funds are accounted daily at the end of the banking day (3:00 pm). This means the Fed may receive your money one day and not send it on until the next.
There are ways for virtually instantaneous transfers, but the Fed charges extra for this. Therefore, it is never done unless specifically requested, and paid for.
Even then, there is usually a delay of one-two hours (Hollywood notwithstanding).
Also, the Fed does no work on Saturday, Sunday, or any Federally recognized holidays. Your money just sits.
With companies like Paypal, there are often additional delays internal to the company. For example, it is very popular for such companies to give the transfer order to their bank after 3:00 pm on Friday. Their bank is still open to receive it, but the day's transfers have closed. The Fed will not accept the money until Monday, and not send it out until Tuesday. Companies do this because, while they can honestly say they have sent the transfer (order), the money stays in the company's account until the Fed will accept the transfer. This gives them two extra days to play with your money.
Chances are, your money will be there Tuesday or Wednesday. If you complain, Paypal will produce the transfer order dated Friday and blame their bank, their bank will blame the Fed, and the Fed will ignore you completely.
You can blame me, if it'll make you feel any better. Of course, it won't do you any good...
When I worked for Mellon Bank, in the Backroom (those familiar with banking will understand), we wrote the program the Fed uses (to this day) to transfer funds between U.S. banks. My part was the human interface.