I just went through the same issue as many others where files were downloading to my laptop even though I had "online only" selected. I just deleted the Dropbox app from my desktop and decided to start over. I newly downloaded and opened the desktop app, and used Selective Sync to only choose some folders to have accessible on my desktop.
But now I want to upload some large files from an external drive to Dropbox online, and not have it go through the Desktop because I think it will cause the same storage issue again. How can I direct the web app to sync with this external drive?