You only get that message if you are trying to load a front-end page on the site – in other words, the internal redirection is not working.
This must be some kind of configuration issue with your site. Try resetting your permalinks: Settings : Permalinks.
If the nonce code you quoted were not working, you would be seeing this message:
Sorry – download must be initiated from admin panel.
And that only happens if the whole session times out, or you have some sort of hack or monitor intercepting the http transactions on your site.
You also might try re-installing Weaver II Pro because your site is acting as if the download.php file is not even there.