Depending on what they are sponsoring, the company will pay several MILLION per year just to have their name on the door. It's advertising, pure and simple. The sponsor (or as Disney calls them - the "participant") will take on a certain percentage of the budget for that particular building and that determines the price they pay for their sponsorship. Certain items are charged to the participant's part of the budget for the building then Disney is responsible for the rest. If a sponsor pulls out then Disney has to then come up with the money to pay for that part of the operating budget for that building from somewhere else.
The sponsors sign multi-year contracts to sponsor the building. Disney has a designated department to deal with the sponsors. Back in the first several years after Epcot opened, most of the buildings had sponsors. The buildings in Future World each had a VIP lounge that was staffed by employees of the sponsor - sometimes along with Disney cast members. The VIPs for the sponsors were able to receive access to the lounge and certain other privileges like front of the line access, free refreshments and complimentary dining reservations depending on the building. Most of the lounges are closed down now or are used for special events. I used to work in the VIP lounge at Seas when UTC was a sponsor. DH and I had our wedding reception there years later after Disney took it back over.
Bottom line - does Disney need the money from the sponsors? Not necessarily BUT why should they pay for something that they can get someone else to pay for? It's just good business.