Problem: A large Excel spreadsheet (about 3MB) which has the "Share Workbook" enabled is used by different authors and over time the file size increases enormously. In this case, the file had grown to about 90MB with only small additions of data over a period of a couple of months.
Possibility: User might have added several empty or almost empty cells to the sheet so that the whole sheet/workbook is filled up.
Interesting observation: Deleting 233 columns (and 64k rows) increased the size of the file by 2MB!
Solution: This happens when the workbook is keep a track of what is being done with it and by whom. If you don't want that information (I wonder how it is viewed), you can remove the extra tracking information by removing the Share feature by going to Tools > Share Workbook and then uncheck the option to make it shared and save it. You can check the size of the workbook after saving and it will be reduced to size needed by the data and formatting.
You can re-enable the share feature after saving if needed.