In outlook 2010:
1) Click the File menu tab then
2) click 'Info', 'Account Settings'
3) on Email Tab, double-click the IMAP account
4) Click 'More Settings'
5) Select the 'Sent Items' tab
6) Un-select the radio button next to 'Save sent items in the following folder on the server'
by selecting the bottom radio button next to 'Save sent Items in the Sent Items folder on this computer'
7) Click 'OK', then click 'Next'
Outlook will then automatically send a test message which can help you verify whether the issue is resolved...
Confirm by checking that there's now only 1 copy of the test email in your local 'Sent Items' folder.