Sent mail is stored in Sent Mail for gmail, but outlook.com stores it in Sent. Both providers automatically copy sent messages, so uncheck 'Place a copy in' in Account Settings, Copies & Folders. You should see a single copy in Sent, but the changes you made might have upset things. Perhaps try unsubscribing Sent, restarting TB, then subscribing Sent again.

Update - I have noticed that if I reply to an email, only one copy is put in Sent; it is when I generate a new email that the duplication occurs.

Apologies sfhowes - I hadn't seen your reply when I wrote my update. Unfortunately, it doesn't seem to have solved the problem; I did as suggested [un-checked "Place a Copy" in Account Settings, Copies & Folders, un-checked Sent in "Subscribe"; closed & reopened TB and re-checked Sent. I sent a test message and have two copies in Sent.

I configure my Gmail accounts to save a copy of sent messages (in addition to the copy that Gmail saves automatically), but I tell Thunderbird to use a Local Folders 'Sent' for that, so the copy saved by Thunderbird and the one saved by Gmail are kept in separate folders. You may want to do the same with this account, at least temporarily, just to see who is doing what.

Just to confirm - I'm using Outlook - not Gmail.

I know, I didn't mean otherwise, but both Outlook and Gmail appear to work similarly in this regard, i.e. both save copies of sent messages on their own, so I used what I do with my Gmail accounts as an example of what you may want to try with your Outlook account, just to see who (i.e. whether Thunderbird or Outlook) is doing what, and you don't try to fix in Thunderbird what Outlook is doing and you have no control over.