Did you take 3 cases? When booking on Easyjet you have to state how many cases you're bringing, if it's a package holiday there will be something on your booking info that will state 1 case per passenger.
easyJet bookings don't include any hold baggage unless you pay for it.
If you booked for two people (PLUS the basic hold baggage allowance) you'd be allowed a total of 40kg spread across TWO bags. (Each person is allowed ONE bag and up to 20Kg but the total weight allowance may be spread across passengers on the same booking). Extra BAGS and/or extra WEIGHT incurs additional fees:
http://www.easyjet.com/planning/baggage
Yes, you have to pay for all luggage with Easyjet, but I think that one suitcase is 20 kgs, not 23. With some other companies, it's only 15 (Thomas Cook and Ryanair). That's what I meant. Now I have to go. I'm flying to Tenerife in a few hours, with Ryanair, and we're only taking one 15 kg bag between us!