This is one save file from a new playthrough with 0.311. No mods. Seems the log file in the save is the culprit, taking 57mb unpacked.That would be quite the bug... I am not sure why that would be the case, I do know saves can get quite large when using a lot of mods but not 13MB big. If you can send me one of these large saves I could dig around in it and see if there is some data being saved that shouldn't.
Actually I think it's not about the old saves at all, but it seems the log file written to a save is not cleared on loading? If you make save 1, load save 1 50 times in a row, then make save 2, then save 2 will be huge. At least when done on the initial admissions page.