I am having the same problem with one of my websites as well.
I use Publicize on Jetpack for multiple websites, and it is only affecting one. The plugin is up-to-date, I have refreshed the connections, deactivated and reactivated it and continue to have the issue.
I do want to note though that the website that is presenting the double posting problem, the posts are scheduled ahead of time. When I publish immediately it posts once to Facebook.
Anyone have any ideas on how to fix this?