Free disk space disappearing; over 130GB "system" files

My partner has a Macbook Air running Sierra 10.12, upgraded within the last 8 weeks or so. In that time we have had increasing problems keeping free space on the hard drive. The free space just continually disappears, to the point where the drive is almost full and the computer stops functioning properly. I've stripped down the user-saved files as much as possible, but whatever new space I make, it just gets filled up. At the same time, the amount of space used up by "System" files is routinely in the 130GB range!! I also have my own Macbook Air, which I haven't upgraded to Sierra, and my "system" storage measures in at only about 50-something GB. Surely Sierra didn't add almost twice as much data to the computer?

When I first started addressing this problem, I found about 20GB in orphaned podcast files that were copied over from older iterations of itunes but never reconnected to itunes. After that the computer had 37GB of free space on it. Since then (a period of maximum 6 weeks) we have not downloaded anything bigger than your standard Word doc or PDF, but the available storage is now in the neighborhood of 1-3GB, and sometimes even going down into the 200-300MB range. *** is going on? Why does this storage keep getting used up? I get that the storage amount is never totally stable and some variations as applications write data should be expected, but going from 37GB to 0 without deliberately adding anything is crazy. Plus, +130GB for system files seems excessive to me.

Here are the solutions I have tried so far:

-- emptied trash

-- stripped down the downloads folder

-- deleted duplicate documents

-- searched for files larger than 1GB and moved to external drive

-- disabled local backups in Time Machine

-- rebuilt the Spotlight index

here's an image of the "about this mac" storage screen.

(yes, iTunes is big, but that size has only gotten smaller in the 2 years we've had this computer, so it's not the issue).

Any help or guidance would be seriously appreciated!!