Parallels taking up over 300GB but Parallels disk is only 128GB. Why?
After a long chat with Parallels support followed by my own investigation, it turns out that the mystery disk space is taken up by snapshots. But Parallels apparently has a bug where it's not correctly reporting the full disk space cost of snapshots.  By deleting some snapshots I was able to reclaim much of the mystery disk space. 

Here's more details. Apparently Parallels stores snapshots in two places: inside your VM's .pvm file (go to /Users/YourName/Documents/Parallels, find the .pvm file, right click on it, and choose "Show Package Contents") : 


in a Snapshots folder, which is what's measured by the green Snapshots area in the General tab of Parallels VM configuration.
inside the .hdd file  that contains the actual hard disk data. If you right-click on this file and choose Show Package Contents, you'll see one .hds file for each snapshot that you have stored. These files are not included in the green Snapshots area in the General tab of Parallels VM configuration.


I deleted several old snapshots using the Snapshot manager, and that freed up 100GB in just a few minutes. Removing each snapshot removed one 10GB+ .hds file from inside the .hdd file.

I did see cases in the Parallels forums where old snapshots didn't show up in Snapshot Manager but were still using up disk space. Apparently there's a Terminal-based way to fix that problem. I'm pasting links here in case others run across that variant of the problem:


https://forum.parallels.com/threads/what-are-multiple-hds-files-in-huge-pvm-file.327942/
https://forum.parallels.com/threads/problems-with-freeing-disc-space-after-deleted-snapshots.328099/


both linking to:


http://kb.parallels.com/9165


I was disappointed in Parallels for not accurately measuring the true disk cost of snapshots.  Had Parallels correctly noted that snapshots were taking up 200GB vs. 128GB for real disk space, the solution (delete some snapshots, dummy!) would have been obvious.  Instead I wasted hours trying to troubleshoot what could have been a simple problem to resolve. 

The support engineer I worked with claimed that this incorrect measurement is not a Parallels bug. I'll leave it up to you to decide if you agree with him. ;-)