It does. I’ve never waited until getting to the airport but if they say they charge 8 quid if you wait, I imagine they would.  

Here’s what they mean. You can have up to 8 bags, but these 8 bags all together must not exceed 20kg. Each bag that you check, if you prepay, will cost 3.99 pounds each, regardless of weight. When you book your ticket, you are given the option to prepay for your luggage.
 
If you do not prepay, but decide to pay for bags at the airport, the same rule applies as above, but it will be 8 pounds per bag. All together, your bags must not weigh more than 20 kg.
 
If the total sum of your checked bags is more than 20 kg, then you will be charged an additional 8 pounds per kg. So say your checked bags are a combined 15kg overweight – that means 120 pounds just for the excess baggage fee. You also have the fee per bag, which was 3.99 per bag if you prepaid and 8 pounds per bag if you did not.
 
Do not be caught out like this idiot (I say that because he is portraying himself as a travel expert):
http://www.msnbc.msn.com/id/18700377/

Thanks for the clarification, and the humorous link. I wasn’t surprised at the extra charge for the bags, but I was confused on the on-line vs at the airport. I wasn’t sure that we’d have access to the internet to check-in, but if it’s a matter of paying when you buy the tickets, that’s easy. Thanks!!

Unless you are an EU citizen, I don’t think you can do online check-in for easyJet. But double-check in case that has changed.