Some "news" sites are so annoying about their ads, I just close the tab and google for someone else's version of the story. I block sites that show up in my news feed often but display more nag than content.
I'm sure in their mind, they don't care about me leaving. Apparently more than enough people put up with it to keep the site viable.
lite.cnn.com is the best lightweight news site I know of, though it is still CNN and probably more US-focused.