Well then I would guess it's a file path issue. Is your stylesheet(body.css) in the same folder as your index page? Or is it in another folder, and you didnt point to it in your link. Also, not sure it matters, but just for the sake of clarity, I dont normally name my files with names that correspond to tags or page elements like "body". Again, I doubt it hurts anything, but just my preference.
Did you actually upload it to your site? It is not embedded in the page and has to be uploaded separately.
Can you give us a live url to look at?
Also you don't have a doctype in your code, and that is a very risky way to build your pages.
PS I agree that it is a bad idea to use a reserved word like body for anything purpose other than its intended reserved purpose. It's just good working practice in all computing to treat reserved words with respect.