I didn't add anything to the image. All I did was use the eraser and erased a few pixels. Then I just clicked on "File", and then "Save". The image was saved as a TIF, just like the original, but increased in size as I described in my first post.
I also tried this: I opened a TIF image, did NOTHING to it, and saved it. The same thing happened...the file size increased from 300 KB to 2048 KB.
I'm confused.