Not an EasyJet issue
This is the normal procedure for "Outsize" baggage for all airlines in Geneva. There is a special area for leaving it off. I do not know what checks it all gets afterwards. During a high-security period at the BA check-in last year, all baggage went this way, nominally being watched over, but in an airport that can be very crowded at times.
With ref to the first reply, I think the new/old low cost terminal will open a year from now. 5 francs lower charges per pax. As I understand it, it could still not happen. I believe a number of the large airlines (LH, Swiss included) have asked to use the LC terminal as well. Easy carries far more passengers than any other airline in Geneva, so pure size is not the issue.
Momo