Can I use the Google Weather API in a commercial project, if I just added a "weather powered by Google" link?
It looks like the Google Weather API is not even an officially supported API, but a 'hack' found and documented by other people. So there is no terms of use that defines if you can use it commercially.
But if you look at a similar API offered by Yahoo, its terms of use explicitly prohibit commercial use, so I wouldn't gamble on using Google's API in your project.