In some cases MXD file size may increase significantly. For example:
File size may be less than one megabyte before the first save, 6.5 megabytes on the first save, 13 megabytes on the second and subsequent saves.
The file size increase may be caused by a large amount of geoprocessing results stored in the Results tab in ArcToolbox in ArcCatalog.
Whenever a geoprocessing tool is run in ArcCatalog, the results are stored in the Results tab in ArcToolbox which persists between ArcCatalog sessions. Conversely, when a geoprocessing tool is run in ArcMap, the results are stored in the Results tab in ArcToolbox and saved within the MXD.
The ArcCatalog Results tab cause MXDs to increase size. When ArcMap starts up, it loads the contents of ArcCatalog's ArcToolbox Results tab into ArcMap's ArcToolbox Results tab. Moreover, if an MXD is loaded into ArcMap, it also loads the Results tab stored in the MXD. When the MXD is saved, the contents of the Results tab are written to the MXD which includes the contents of the Results tab from ArcCatalog. All of the contents written to the MXD can be an issue because it is common for the Results tab to contain many geoprocessing results, potentially spanning many months, which may cause MXD 'bloat'.
If many geoprocessing operations are performed, it is good practice to occasionally clear the Results tab in ArcToolbox in ArcMap and ArcCatalog on a regular basis. They are not cleared automatically by the application.