Gallery and Google Photo Syncing Samsung S5. I have Google Photos set to backup my Pictures folder when on WiFi and power.

Day 1: Take several photos. Backup takes place overnight. 

Day 2: Take more photos and delete some photos from Day 1 from device. Backup overnight.

Day 3: All Day 1 and 2 photos are in the cloud. Those I deleted from the device are not/never deleted from the cloud.

How can I get Photos to sync with Gallery by also deleting photos I've deleted locally?
Depends on your Google Photos app version. As of v1.23, deleting local gallery photos should prompt you -- Read more about it here

As quoted in the article --


  Say you took a few photos on your phone and they're already backed up
  to Google Photos. Then you went through another gallery app (if you
  use the Samsung or LG or HTC Gallery apps or another third-party
  client) and deleted the ones you didn't want to keep. The images would
  still be backed up in your Google Photos account.
  
  Now, Photos is smart to realize that this has happened and suggests it
  removes them too. For example, you may want to do that for burst
  photos that you don't want in your account or for random shots that
  you only needed for a couple of days. But you don't want to do that
  for photos that you want to save but just removed because you're
  freeing up space on your device. That's why it's great that this is an
  optional card and not an automatic action.


You've set up google photos to backup over wifi and when charging. So the next day you delete the photos via a different gallery app, google does not have an idea that you've actually deleted them locally.

If you want to delete local copy while retaining the cloud copy, continue what you're doing now.

If you want to delete cloud + local copy, one of many ways would be to delete it from the photos app.


Open photos
Select the photos you would like to delete
Tap on the 3 dot overflow menu on the top right of the screen
Select "delete device copy"
Tap on the bin icon at the top to delete the cloud copy as well.