On 10 May 2014, at 23:09, Matt Neuburg wrote:

[…] When I open my project, the same two tabs are always open. Why?

From release notes:

The state is stored in ~/Library/Application Support/TextMate/RecentProjects.db so you can delete this file to clear all state. You can also bring up the File → Open Favorites… dialog and press ⌘⌫ for each entry where you wish to clear the saved state (and remove that folder from the history).