Game file saves will depend on how many leagues you have running, size of player database, if keeping retired player history etc. As mentioned try compressing saves, will take more time
Save files of 2GB (GigaBytes) looks very excessive. I have a custom database (a lot of players) and around 11 active leagues and my save files are around 180MB (MegaBytes)
Edit - Its likely that your PC may have run out of space so consider deleting older / unwated FM game saves, other unwanted data on your PC