How many accounts are defined within Outlook? Are they pointing to the same
mailbox? Even if you have different login credentials for both, are they
for the same e-mail provider (some provide a "family" account with aliased
logins but they all go to the same mailbox so it is shared amongst these
multiple logins).
Do you have superfluous scanning of your e-mails enabled in your anti-virus
program?
Is the duplication in the Inbox folder(s) or are you looking at some
"search" folders defined in Outlook?