Dropbox keeps trying to download and sync files set to online only

No, you're not the only one with this issue. In case you didn't see my earlier replies:

Precisely!

In case you didn't see my earlier message:

I read your whole thread with complete empathy. I have been facing this issue for years. I've even tried TWICE in the past years to contact Dropbox for help (I got tickets too!). Basically I've now given up. I've been told so many times the explanation that it's because something I do on my laptop activates some folder in Dropbox, though sometimes it really can't be possible, because I'm doing something totally unconnected to the folder that starts to sync. And mine happens any time, not just on Fridays. 

I've followed online threads on this issue (not many - this is the clearest) but no help. Or so technical the discussion that it loses me. 

I've resigned myself to conclude that the Dropbox people don't know how to deal with this, or it's such an obscure issue they're not looking into it - they just repeat the same message to me about .... what you said. 

And yes, many times my laptop says that I'm running out of space. At that point, I know that Dropbox files have started downloading / syncing AGAIN, and I just have to go set them to "Online only" AGAIN, and AGAIN and AGAIN. Sometimes I just forcibly PAUSE syncing to give myself peace of mind

Oh ok I just saw your comment about "don't open File Explorer" while Dropbox is being used. Wow. Maybe I shall try that. But File Explorer is like so essential to my work! But you're the first one with a different concrete doable suggestion, so I'll try that anyway.