What am I missing? Is there anyway to get a bigger screen in full screen?
When it goes full screen it will turn off window borders etc and then ask your display driver to change resolution. I assume it's currently set to 800x600.
You will either need to change the resolution in the settings that it uses for full screen, or change your display driver settings to automatically stretch all resolutions to your native size. I would suggest you doing the later anyway because having a postage stamp size image in the middle of a screen is largely pointless.