Adding signature to photo decreases its file size

Where are you seeing the file size reduce?

Editing in photos does not alter the original file. Instead the edits are recorded in a database, and a preview image is generated.

The only time a smaller file can be generated is if you export the image out of photos. If you do that by drag and drop, it only uses the preview images which can be much lower quality.

If you use file>export, you can choose the files size, type and quality.

When you edit a jpeg photo in any manner and save that edit you'll recompress the jpeg and it will be smaller in file size than the original.

However, when you export the edited version out of the library you can use the JPEG Quality menu to set the file size. High will be about the same as the original JPEG and Maximum will be larger as it totally uncompresses the original JPEB file.