Adobe Lightroom, GIMP, Aoao Photo Watermark, Mass Watermark.
It may be possible but I have never seen it done.
You are better off resizing the images (or copies) for consistency in display, before watermarking.
eg. 160, 800 & 2400 width for thumbnails and different screen sizes, then you can watermark the larger ones with guaranteed results.
When you batch watermark images, can the watermark be auto resized to fit the images in different sizes?
