Time Machine failing: "an error occurred while copying files"
Looking for backup errors in the log, what I found was ; backupd[3278]: objc[3278]: __weak variable at 0x7f9227c07600 holds 0x7f9227c00003 instead of 0x7f9227c0e060. This is probably incorrect use of objc_storeWeak() and objc_loadWeak(). Break on objc_weak_error to debug

Searching for these terms, I found this solution, which solved my issue: https://discussions.apple.com/thread/7686484?start=0&amp;tstart=0

theperlarsen Dec 27, 2016 9:40 PM in response to theperlarsen  Level 1 Level 1 (4 points)
Dec 27, 2016 9:40 PM in response to theperlarsen
SOLVED: Turning off iCloud Drive fixed the issue for me.

The weak variable error in the console is misleading. The logging mechanism was changed for macOS Sierra. Use the paste command into a terminal to view time machine errors:

log show --predicate 'subsystem == "com.apple.TimeMachine"' --info --last 4h | grep Error

I saw lines containing starting with:

Error: (-34) SrcErr:NO Copying Copying /Users/myusername/Library/Mobile Documents/ ...

The mobile folder is used by iCloud drive, so I turned that off. That allowed the backup to complete. Hope this helps others that are experiencing this issue. Hopefully the final version of 10.12.3 fixes this.