If you're referring to the gray area on both sides of the Awesome Table editor (image below), that's the natural constraint (approximately 1,100 pixels) while on live view mode (this is noticeable if you’re using a high definition [HD] device with high native resolution). This cannot be manipulated within the Awesome Table editor or Google Sheets template.
Once the view is embedded on a live website (Google, WordPress, Weebly, ...), the actual view-span will expand - depending on your CSS layout. This is because the actual span or width of the embedded Awesome Table view uses the Responsive Web Design system. This means that the rendering of the span or width of your view will depend on the CMS or website builder. More specifically, the theme and/or layout used.
View-span comparison between the editor and embedded view using full-width body layout.