I use Thunderbird to manage 2 email accounts, personal and business. I was having the same problem with my business email and realized I was having Thunderbird save a "copy" of a Sent email when, in fact, Sent emails automatically save in the Sent Mail folder (duh {forehead smack}...that's why it's the Sent Mail folder)

In Account Settings, under Copies and Folders, UNCHECK the box next to "Place a copy in:" under the "When sending messages, automatically" heading.

I did this and sent an email from my business account to my personal account. No duplicate email in the Sent Mail folder...just the original Sent email. Funny thing is I had the exact same settings for my personal email and a duplicate Sent email only appeared one time, and I send more email from my personal account than I do from my business account. Changed those settings too, just to be safe.

Did you check the box 'Place a copy in' in your Account Settings? If so, uncheck it.