This blank space appears because WebEasy works with fixed page sizes, while you can resize your browser window to any size.
The solution really depends on what will fit in with your page design. You may find it suitable to enlarge your pages - this can be done by clicking the "Page" button in the left toolbar, clicking the "Size" button in the top toolbar, then entering a new size.
Alternately, if you have WebEasy Professional, you can set up your site so it is centered on the screen at all times:
1) Open your site in WebEasy.
2) Go to the "Build" menu and select "Preview".
3) Click the "Options" button.
4) Check the "Dynamic HTML" box.
5) Click the "Advanced" button.
6) In the "Web Site Style" box select "Centered on full screen (Kiosk style)".
7) Click OK.
8) Click OK again.
9) Click OK again to preview your site.