Time machine backup hangs
In my case, I confirmed the drive was working fine and could easily do almost 100MB/s, yet backups were happening in KB /s.  I had backups going back 4 years and it seems it is the layering of backups that slowed things down.

A few possible solutions:


Many users report that booting into "Safe mode" will reset some data and then restarting back into "Normal mode" may solve such issues.
Try to repair the external disk using "Disk Utility" (may take a very long time).
Can try updating the drive firmware.
If you have enough space on the external drive, partition it into 2 separate disks. (May also take a day or so)


Then setup Time Machine to use the new partition. This will require a complete "Initial" backup, but in my case, 300GB initial backup was still faster than the 4GB incrimental backup on the old drive.

As a final resort, wipe the drive and backup from scratch or buy a new drive to use in parallel.


I'm still experimenting, but there may be a bug causing Time Machine to slow down significantly as new backups are added. I'm using an HFS+j external USB3 drive from WD. Hope that helps.