Since you didn't mention MS Exchange in your original post, there's no
way for me to know you are using MS Exchange. Have you talked to your
Exchange admin to determine from their logs if you are sending any
e-mails to the same recipient after the first one that you sent? Maybe
they can enable logging specific to your account now, watch for a couple
days, your friend continues to receive duplicates, and then check the
log. Just don't send anything during that test period to that recipient
to make it easy to do a search. If it's not going out of your company's
MS Exchange server again and again, the problem could be with your
company's ISP (in which case you will need to get your Exchange admin to
talk to the company's ISP).
Have your friend use a webmail interface, if available, to check their
e-mail account with their ISP to see if your message is still sitting in
their account (so the screwup is at their end because they are leaving
the message on the server while pulling a copy of it).