Duplicate attachments appear on cases.
Depending on your E2CP configuration, attachments may be stored on the email, the case or both. If you have the Force.com Labs Email Attachment Reassigner package installed, it will also copy any attachment on an Email Message to its respective case. Simply uninstall the Force.com Labs 'Email2Case Attachment Reassign' package because it is not needed when using Email to Case Premium.
This issue is by design due to a duplication of functionality in Email to Case Premium and Force.com Labs Email2Case Attachment Reassign.