You might want to remove the Gmail account then add it back. This often fixes issues with Gmail accounts.
Do you see folders like this under Gmail in the folder list?
If yes,
Under Mailbox in the Menu bar, select Use this mailbox for....
You might want to log into Gmail in your browser. Under Settings Labels, clean up the folders under Circles. You might find several sent, trash and draft folders created by some email clients. By default Gmail stores all your messages in the top Sent folder on the server.
BTW, Mavericks Mail is trying to get around the oddities of Gmail IMAP. Results vary for users.
You might like MailTabPro for Gmail $1.99. In Mac App Store (MAS). If you are low on disk space this is a great option since you don't download messages..
https://itunes.apple.com/us/app/mailtab-pro-for-gmail/id430252530?mt=12&ign-mpt= uo%3D4