From the image of the Windows Explorer interface below it seems that file geodatabase sizes are not ~addressed by Windows Explorer... ??
Having that information available from the FGDB for Windows Explorer and other NOS operations would be helpful.
Also it seems that the Date Modified setting might be getting updated when ArcCatalog views the data since I viewed the NeedsAnalysi_FGDB_V9x.gdb at approximately the time noted in the image??
Also it seems that fgdb are addressed by Explorer as directories although they are not......