Check your settings in BIS, there is option to "Auto BCC" yourself of outgoing email from the BB. This will explain you getting a copy as if you emailed yourself. https://bis.na.blackberry.com/html?brand=nextel
Not sure why the person you email is getting 2 emails of the same message. If its just one person or multiple people, have them check the message header to see what email address's are there. This issue may be on there end.