why would a file shrink in size by 50%

I am working on a 300+ page manuscript in Libre Office Writer. I printed a hard copy and made corrections, and started making corrections in Writer. When I got ready to back it up, I noticed that the file size was now 393 Kb, where my two backups are each 803Kb. I made only minor changes. The page and word counts are accurate and in line with the backups. I printed out a hard copy; all the pages are there and I don’t see any formatting changes. (It’s basically just text anyway.)

I don’t want to lose anything I have written, but I can’t see any change that would lead to this disparity.

Is your file saved .odt?

Reasons could be graphics images saved in lower resolutions, images linked from disk instead of embedded in the document, cleared change tracking if it was enabled, embedded font not embedded now, previous copy saved as versions but not now, …, probably some more I didn’t think of.

If it’s mostly text then you can try to compare documents, load the newer file and then choose menu Edit → Track Changes → Compare Document… that doesn’t pick up embedded objects or graphics though.

You could also get a rough first overview of at least what in the zip has changed by executing unzip -l oldfile.odt and unzip -l newfile.odt and comparing the two file listings (don’t omit the -l as otherwise you’d extract the files to disk), or use some graphical zip-archive manager to list contents if you don’t have the unzip tool or you’re not acquainted with the command line.