You can use all available weights like "light" of any Google font, but it's a little manual if not listed in the Web Designer UI.
In Google fonts, select all the weights you'd like to use and generate a LINK tag, copy this and in Web Designer > Code View paste to replace/overwrite the existing font LINK tag.
Then in Design View, to use weights not appearing in the UI, select your text and use the CSS panel to assign a font-weight value like 200.
Hope that helps,
Kent
Google Web Designer team