ThumbsPlus identifies image files by their name and location, and it matches the files to their thumbnail records that same way. So, image files thumbnailed through their network location are considered separate from the same files thumbnailed through their local path. That explains why your keywords only show up with the thumbnails that were created through the network path.
> I want to keep my media backup up off site, say, with Google Drive. Here's my question: Is there any reason I shouldn't simply drag my Pictures and Vidoes folders (in my Library) to my local Google Drive? Or...
No, just be careful not to move them (instead of copy).
> So, should I just drag the Network folders (Pictures and Videos) to my local google drive location....
If these are just a backup, it doesn't really matter how you copy the files. If you use ThumbsPlus to do it, it will also copy the thumbnail records in the database (including keywords if you copy them from the network folder). That would allow you to browse your backup images in TP and see their keywords, but I'm not sure if that would serve any practical purpose. The general purpose of a backup is being able to recover from data loss. Well, if you lose a file, you can just copy it back from the backup to your working folder (doesn't matter how you copy it) and it will be restored, and ThumbsPlus will show its thumbnail record (unless 'automatically remove orphans' was on and TP had noticed that the image file went missing - in that case it would have deleted its thumbnail record).
> [...] and then just delete the Pictures and Videos folders from the Library?
I'm not sure what you mean by Windows Library. But don't delete any image files from your harddisk if you plan to keep working with them! :)