Experiencing double emails in your sent folder of your outlook.com email address? I had the same issue when sending mail from Thunderbird via outlook.com SMTP on a custom domain (via domains.live.com).
Luckily – the solution is very simple. It seems that Outlook.com automatically places anything sent through their servers in the account’s sent mail folder, most mail clients by default are configured to place a copy in the sent folder. While this is required with Gmail with Outlook.com it is redundant and should be disabled.
Once you’ve done that feel free to manually delete the duplicates.