Why Dropbox did this to us is not known, but it’s one of the things that made Sync very difficult to develop. If it hadn’t been for that, Sync probably would’ve been out 2-3 months earlier – it meant I had to rewrite large parts of the plugin and (of course) test exhaustively, fix problems revealed by the testing, etc etc etc. A better design for Dropbox syncs is in the works.
I suggest closing all of your databases on DEVONthink and trying to import from that location in the Sync Preferences. Are any databases listed multiple times?
Not that I know of, unfortunately 
I tried that but before I get to the list, I am getting an error message (see attached): “There was a problem fetching the remote databases”.
DT error.tiff (22.2 KB)
Hmm. Okay, some sync failed at some point in the past and is now messing us up in the present.
You’ll have a number of folders in Apps/DEVONthink/databases/. One of these is @inbox, which corresponds to the Global Inbox on every instance of DEVONthink that you sync. The rest will be UUIDs – something like 0123ABCD-0123-ABCD-0123-ABCDABCDABCD.
One or more of these folders will be missing a file named “metadata”. I’d check the @inbox folder first. If the folder doesn’t contain a file named “metadata”, just delete the entire folder. The “metadata” file is needed for the folder to be recognized as representing a valid database, otherwise an error is thrown and syncing to it is impossible.
That worked, thank you. So now all the databases show up in the Import dialogue. However, each database only shows up once, so still no idea where the leak is.
I contacted Dropbox for some help in identifying the folder that hogs space. Will report back here (unless you have other ideas in the meantime).