The size of your exported slideshow is set inside Lightroom before you export. In the edit panel area you'll see an "Output Settings" section. Toggle it open if closed, and the first group will be "Slideshow Dimensions". It includes options for Scale, Fixed Width/Height, and Offset.
With Scale set to "Fixed" (the default) your exported slideshow will display in the HTML document at the exact dimensions entered for Fixed Width and Fixed Height. If you include the Header or Wet Floor effect in your slideshow, the height of the SlideShowPro Player will decrease to provide room. Increasing the Fixed Height of the slideshow will provide more room for slideshow content.
New in v1.9.8.7 of the plugin is "Fluid" scaling. This embeds your slideshow in the HTML document so it consumes the entire viewport of a user's browser. The slideshow will automatically scale / realign internal elements if the user expands or contracts their browser window.
When using "Fluid" the values entered for Fixed Width/Height are ignored and the Offset sliders are enabled; allowing you to push slideshow elements away from the browser's viewport edge so that they aren't crammed-up against it.
If using "Fluid" for Scale, there are a few parameters you may want to change for improved appearance and image quality.
One, if you want viewers to see your photos as large as possible right from the start, check Expand Browser Window in the Options box. This will automatically force a user's browser (all except Google Chrome) to the width/height of their screen.
Two, if you are loading content from SlideShowPro Director you should scroll down to the Director Publishing box and change Large Publishing to "Full Screen". What this does is instruct SlideShowPro Director to generate images for your fluid slideshow that are the same dimension as the end-user's monitor. This provides the largest possible images for your fluid slideshow and will provide better quality results if a user scales their browser window.
If you are loading content from your local Lightroom Library (and not Director), you should export images that are large enough for fluid viewing. Scroll to the Image Export box and increase the Large Width/Height settings to a higher number (around 1680px for both is a good middle ground).