This feature does work, and works well, and is indeed on the the best features of Weaver Xtreme Plus. The steps for using Google Fonts should be very clear, but if you are using other font sources, it is easier to get one of the entries wrong.
If you don’t have all the new font settings exactly correct, the font may show up in the drop down font lists, but still not be loaded corectly.
If you provide a link to your site, we should be able to help.
One thing to try just to prove to yourself that it will work, try selecting one of the pre-defined Google Fonts and using theme in a test.