I understand what you are looking for. I honestly never cared much about how light it was or no because Linux is already so light compared to Microsoft. 
I think according to this the XFCE version is the lightest version of Linux Mint. I mentioned earlier that I got worse battery life than WIN10 with the XFCE version, so theoretically MATE would have a little worse battery life than XFCE, and Cinnamon would have worse battery life than MATE unless I am overlooking something.
It was never a big priority. But I am running Mint “Cinnamon” and it is pretty quick and lighter than the Debian and Fedora. Cinnamon is actually the Gnome Desktop.
Battery life IS a big priority to me though, so with that said, which version should I be running? Thank you for your attention to this matter.
Again I do not know which would be the easiest on your battery because I am never that dependent on my computer when mobile and hardly ever use it. But you may be asking for too much. The best I ever got out of a laptop battery “using it” was a couple hours unless it was sitting there asleep/hibernating. But if it is just going to sit I turn it off. So if you are getting more than three hours that is already incredible. I’m not sure in the real world I have ever heard of getting much more than that.
So I guess I can’t help much with that...