G'Day
The actual spreadsheet may be bigger than you think. There may be cells, a long way from where you think the boundaries of the spreadsheet are, that have single spaces in them. Just to check, open the spreadsheet and press Ctrl+End and see where you end up. You may end up in some ridiculous location like AD400 or something. Where ever you end up will mean there is a cell in that column on some row with a value in it (space is a value) and a value in a cell in some column in that row.
Make a backup copy then try the following:
Make sure the sheets are Ungrouped - you want to do this one sheet at a time. Try deleting all the rows from the last row +1 that you use to the last row Excel thinks is the last and likewise from the last column+1 (you) to the last column (Excel); do this for each sheet and delete "blank" (unused) sheets and then resave it. See if that reduces the size of the file.
This can happen if the spreadsheet has become smaller over time but people have just typed in spaces in cells that become unused instead of deleting the cells.
Geoff