Is there any way/addon to "automatically" change the browser size?
I don't use an add-on. Instead I use a small stand alone program (freeware):
Resize Browser is a tray icon testing utility for anyone doing development for an Internet browser. This utility allows you to test your code within all of the default Windows screen resolutions, without changing your own resolution. It simply resizes any browser window to 640x480, 800x600, 1024x768 or any custom size. This will allow you to verify your html or application at different screen resolutions.
This is a must have utility for any web developer or application designer. There are options that allow it to stay on top, account for the Windows taskbar, center the browser within your current screen resolution or auto refresh the browser list. Download Resize Browser today, its FREE! Click here to download Resize Browser v1.04 .
Source Resize Browser v1.04
I am not affiliated with RJL Software in any way, I am just an end user of their software.