Hi Michael,
I have seen this happen when hosted on a Mac or Windows server. The Google API is accessed using a secure HTTPS connection, and sometimes the right plugin is not installed into the web server to allow that to happen.
I did try at one point to display any error messages that are returned by Google for additional clues, but the return codes were not easy to decipher and Google did not publish what the format was, so I left it.
There may also be some clues in the error logs of the web server.
However, you won’t be lacking any fonts or weights or styles, as they are all in the fallback file. Google is long overdue an update (they have a load of new fonts waiting in the wings) and I’ll keep my eye on that and provide an update when they appear.
There beta release linked in another ticket will display some additional error details from the Google API. It may be worth giving it a try to see if it tells you what is happening:
http://ww.wp.xz.cn/support/topic/control-which-weights-get-downloaded?replies=3
The release that should tell you more about the error has been out for a week now. I’ll assume your install is working, and will close this ticket, but feel free to reopen it with more details if you are still have a problem.