I once took an elderly neighbor and her husband to the airport, and thank goodness I stayed with them to help. She had put all their stuff in one suitcase, which weighed 28kg- and EasyJet said she had to leave stuff with me, or not travel. They were distraught - fortunately there was a shop that sold luggage at the airport, so I run there to buy another case so they could transfer enough in the new one. Due to his medical needs, and the fact they were going to a wedding, they didn't want to part with anything.
It was explained to us that the maximum weight is for health and safety/Union regs for luggage handlers -makes sense, really.
When we travel with EasyJet, we take one suitcase for the 2 of us, and 2 small wheelie cases for shoes, heavy stuff, so we only pay for one luggage fee.