If you have multiple accounts in Microsoft Outlook they need to be separate accounts. Make sure they are not aliases of the same mailbox. If the email account is an alias that means you have the same account that is configured twice. This means emails being sent from either alias will be received in the same mailbox, which results in double emails.
To understand aliases think of it as different ways to send mail, such as you can send mail to more than one person at a mailbox, or you can reach more than one person at the same phone number.
You also have an option during configuration to leave a copy of the mail on the POP3 server. If this option is chosen both accounts will receive the same email, which will give you duplicate emails. To stop these duplicates open Outlook and click on Tools and Options. A dialog box will open and you will see different tabs at the top. Click Mail Setup and click Send/Receive. Click on Edit and select the alias account. Uncheck the Receive mail items box.