Are you able to confirm the software that you purchased from X-Plane i.e. Ultra Weather XP, xEnviro etc. and is it a plugin, or something else i.e. the default weather program within X-Plane 11 itself?
Also, is the issue that a) it will not download from the internet (as per your original post heading??) or b) that it does download from the internet, but doesn't actually load when opening X-Plane 11.exe?
Could you upload your X-Plane Log.txt file as well as your C:\X-Plane 11\Custom Scenery\scenery_packs.ini file
If the weather package that you purchased is a 'plugin', then the order in which the plugin files are written in the scenery_packs.ini file are very important!