I already have a window open with the web site I'm debugging. I don't need VS to launch another one for me every time I need to debug.
Is there a way to stop this behavior?
Open your startup project's properties (Project → {ProjectName} Properties... from the main menu or right click your project in the Solution Explorer and choose Properties), then navigate to the Web tab and under Start Action choose Don't open a page. Wait for a request from an external application.
You will still be able to use any browser (or Fiddler, whatever) to access the running application, but it won't open the browser window automatically, it'll just start in the background and wait for any requests.