I may have found an answer:
If you are signed in to "Windows Live Mail" (which is a button on the "home" tab of Windows Live Mail (on the DESKTOP version)), the DESKTOP version will get any mail you have set up to receive via your Windows Live Mail ONLINE/WEB version.
Of course the desktop version will ALSO be checking any accounts you have setup within the desktop version.
In my case, my Windows Live Mail WEB version was set to check my Yahoo Mail.
And...
My Windows Live Mail DESKTOP version was ALSO set to check Yahoo Mail (as well as my GMail).
Emails sent to Yahoo appeared twice...emails sent to GMail appeared once.
I signed OUT of "Windows Live Mail", via the button in the desktop version,. and PRESTO, I'm now getting just one copy of any mail sent to my Yahoo address.
Hope this helps.