The New York Times twitterers share some of their lessons of 2013 on the Nieman Labs:
During 2013, we began consistently scheduling multiple runs of tweets highlighting some of our best enterprise material, especially during weekend hours and overnight, when @nytimes is mostly automated. It goes without saying that if you tweet more, you’ll get more traffic overall. But what we found when we scheduled tweets on Saturday and Sunday was that the average click per tweet grew substantially.
One thing that this means is that Twitter users who follow all sorts of media accounts (and not just the national media), can expect to see tweets repeated.