Here are a few tips which should hopefully help to clarify a few things.
If you create a gallery with the Lightroom plugin and then edit it in JuiceboxBuilder-Pro to create a multi-size image gallery, then the images that Juicebox will have to work with are the images in the gallery's 'images' folder. When resizing images, JuiceboxBuilder-Pro scales down large images but does not scale up smaller images so if the images in the 'images' folder are already smaller than the maximum image bounds for the specified image sizes, then they will simply be copied across to the gallery folder as they are without being upscaled. Therefore, make sure that Lightroom exports images large enough that they have to be downscaled by JuiceboxBuilder-Pro.
When displaying a gallery in Large Screen Mode, Juicebox displays the Medium size images in the standard gallery. Large size images are reserved for use when the gallery is expanded fullscreen (via the Expand button on the Button Bar) and for when an individual image is opened in a new window (via the Open Image button on the Button Bar).
For more information about Screen Modes, please see here.
For more information about Multi-Size Image Support, please see here.
When a gallery is displayed by Juicebox, the images are scaled within the gallery's image area according to the imageScaleMode configuration option (found in JuiceboxBuilder-Pro's 'Customize -> Main Image' section). By default, its value is SCALE_DOWN. Images larger than the image area will be scaled down (respecting the image's aspect ratio) but images smaller than the image area will not be scaled up. Alternative values for this configuration option (and short descriptions of each) can be found in the Main Image section of the Config Options page.
Images within a Juicebox gallery will only ever fill the image area within the gallery. If you want your images to cover the entire screen, you will need to disable gallery elements for which space is reserved, such as the thumbnails and make sure that other elements such as the caption area, the Gallery Title and the Button Bar are either disabled or displayed on the overlay (rather than in positions outside the image area). You may also need to set imageScaleMode="FILL" (although this will crop images unless their aspect ratio matches that of the image area).