Encrypted image duplicates backup in time machine
Time Machine backups files as seen in Finder, it can't look inside your encrypted image. So every time you modify the image (even just the access date of some of the files in it) TM will register the image as a changed file and backup the whole image again.

You can exclude folders in TM preferences, so you could move your image into a dedicated folder and exclude it. And then use other means, e.g. a USB drive, to backup the image manually.

You could also use DiskUtil to create a new encrypted image as a "sparse bundle" and move the confidential content into this newly created image. Using the "sparse bundle" format should, in theory, allow for a more granular update record so TM doesn't need to backup the whole image each time. I had some mixed experience with this in the past though.