This is an "updated" Photoshop CC when I went to Windows 10. When I used to save in the pre Windows 10 Photoshop CC, I would get a file size abouit what you describe above, however, it seems as though I have also lost my "Save to Web" option, not that I ever used it as that strips off EXIF data.
Anyway, my workflow is: After converting to 8bit, I go to "File" - then "Save as" - then select jpeg, and save which then takes me to the "jpeg options box" which has the slider scale of small through to large file 0 through to 12 and even at 0 it is saving as a file which os 1.44MB! Very strange!