Thank you for the link.
I see the problem in your own gallery but I have not been able to replicate the problem in a test gallery of my own (using 'Small' and 'Medium' images of the same dimensions as yours, the same configuration options that your gallery uses, the same 'index.html' page code and the same version of Juicebox-Pro).
If it's any indication of the problem, if you open one of the images in a new window (via Juicebox's 'Open Image' button), the image is still displayed very small. After clicking the 'Open Image' button, the image is displayed directly in the browser (with no HTML code at all) and Juicebox is no longer part of the equation.
On a retina display mobile device, the 'Medium' images should be displayed in the gallery and it should also be the 'Medium' images that are opened in a new window.
I would not expect to see such a small image when opened directly in a browser (your images do not appear to be that small).
I don't see anything obviously wrong with your gallery and cannot replicate the problem myself.
The most obvious difference between your own setup and mine is the web server so I'm wondering if there might be something going on server-side that is somehow causing the problem.
Maybe there's some server-side caching going on or perhaps use of a CDN which is currently serving older, smaller versions of your images.
It's all I can think of at the moment. If I think of anything else, I'll be sure to post back.
In the meantime, try creating a fresh gallery with different image ilenames that you know have not been cached anywhere (just rename your images) to see if this makes a difference.
Also, although there is no reason why your gallery with 'Small' and 'Medium' images should not work well, you could try creating a gallery with just 'Medium' images to see if this helps.