Is this the first backup you have done? And what software are you using for that?
No disk cleanup/maintenance/repairs can definitely be an issue. Also, when you have "upgraded" to a new OS (example: El Capita to Sierra), did you do the upgrade "in place", ie, have Sierra basically "overwrite" El Capitan?
What you might try and do is download the excellent freeware program Onyx, from here:
https://www.titanium-software.fr/en/onyx.html
Make sure you get V3.3.0, which is specifically for Sierra. When you install and run it, one of the choices is "Maintenance", and there is one entitled "Permissions". Run that a few times. Also, do the two other maintenance tasks "Scripts" and "Rebuilding". Then, click on "Cleaning", and run all of them except "Erasing". See if that helps.
Also do some disk cleanup on your own. Owning and maintaining a Mac is just like owning and maintaining an automobile. Heck, I have a 2013 Toyota Camry (second Camry we have owned), and just like Macs, just about all Toyota cars are rock solid, and in particular, Camrys. But, I make a concerted effort to take care of it, both with my own efforts (ie, some "simple" maintenance) and bringing it in for scheduled maintenance. Just like my Macs, the car runs flawlessly!
I run Onyx once a week on both of my Macs, and I would not be without it. I also use the excellent commercial program Tech Tool Pro on both of my Macs for more "extensive" disk cleanup/maintenance/repairs. It normally retails for $99.99, but it is on sale now as part of a package of apps for less than half that. This link is where I saw it a couple of days ago:
https://shop.macworld.com/sales/mas...t-you-want-fab-5-mac-bundle-ft-techtool-pro-9
But you better hurry, as there are only 3 days left for that sale.