Well, in any fantasy RPG they play a little fast and loose with actual physics. But based on it's volume and the density of steel that is what it comes to.

As for trying to figure out what it weights logically, I know quite a bit about actual sword mechanics and construction, as well as physics involved in martial arts. There really isn't any way to reconcile what is happening in the game with real life. It's best to just enjoy it for the ridiculous spectacle that it is.