That seems strange. Did you change the format of the images? The only other possibility I can think of that might change the file size is if you have tagged the photos in the Organizer. I'm guessing that when the batch renaming takes place, the metadata is also written to the file. But that would be a very small change in size. Has this happened more than once?
The issue is linked with the way jpeg files are compressed in size.
Usually, changing the name of a file is not considered an edit of an image such as the edits made from the editor, that change is change in the file as it is known to the Windows explorer, so you don't use the 'process multiple files' command of the editor, you rename from the Windows explorer. Only the name is changed, the jpeg file image is not decompressed, edited and re-compressed when it is saved. With the editor, the batch command above can apply several changes at the same time, changing format or size for instance. In such cases, it's logical to be able to rename the file at the same time.
Re-saving a jpeg will always produce a bigger file size in kilobytes if you choose the best quality (low compression) option in the process multiple file dialog.
You don't use the organizer which is the tool for renaming your files without changing anything to image (no jpeg decompression and recompression), only a change in an orientation tag in the metadata header of the jpeg files. That's what the Windows Explorer would do ; the organizer does the renaming while keeping the links in the catalog to the new renamed files. Unfortunately, the renaming templates in the organizer are less flexible than those of the editor.