The userscript helps you find larger images for currently ~3700 hardcoded websites (using ~2100 rules), but it supports a number of generic engines, which means it can in theory work for almost any website.
Some of the websites it supports includes:
Social media websites (incl. Instagram, Pinterest, Twitter, Tumblr, Weibo)
News websites (incl. BBC, Daily Mirror, Huffington Post, The Guardian, The Independent, Vogue)
The pop-up and the preview might take a few seconds to show as it currently needs to download the entire image before being able to display it.
You may encounter a warning from your userscript manager that the script is performing a cross-domain (or cross-origin) request.
The script will request the generated URL before redirecting or previewing, to either ensure it exists, or download the image (if using the pop-up). Cross-domain requests are also used in API calls, such as for Flickr, DeviantArt, and Reddit.
If you want to see exactly what happens, search for do_request in the userscript.
Why does it redirect to a smaller image?
Sometimes websites will scale images up, so this will return the original image. However, if the first image is indeed larger and isn't scaled, please file an issue, and I will fix it ASAP.
Why does it redirect to a scaled-up image?
Most likely because the original image is scaled-up. I try to make sure the script doesn't return any URLs that will scale up an image, but if you believe there's an error, please file an issue.