Hi,
What exactly do you mean by "re-delivering"? What changes/steps have you performed recently, which has caused Outlook "re-delivering" old emails?
It might be due to a corrupt identity in your Outlook 2011 for Mac. You might consider re-creating your email account in a new identity in Outlook 2011 for Mac and verify whether it helps to fix your issue:
https://support.microsoft.com/en-us/help/2360509/rebuild-the-outlook-for-mac-2011-database-to-resolve-problems
Regards,
Ethan Hua
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