While you're there check out No. B06, the "playboy rapier".

From Petersen's "Norwegian Viking Swords":

Type C: These swords are among the heaviest of all the swords from the Viking Age. I have thus weighed a sword here that [~66] weighed 1.896 kg. (C 777 Vik, Nes, Hallingdal), making it the heaviest of the swords that I have tested. It is probably only type D that can measure up to our type [C] when it comes to weight.

Type D: Even though none of the swords have the entire blade preserved and therefore not their full weight either, they are nevertheless among the heaviest swords of the Viking Age. C 8095 weighs 1.476 kg and C 1977 weighs 1.346 kg.

Obviously, not all swords were feather light. Unfortunately I don't have "Swords of the Viking Age", there's propably much more info on that.

I want this one...

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This is just speculation, but perhaps the original was made for a specific purpose. Some of the early Viking-era armour include lamellar over maille. That would have provided some pretty hardy defense. Of course, only a king could have afforded all that metal… A big, heavy sword might have been better for killing a king. So the sword could be a “king killer”.

That is, again, just my wild speculation. From the looks of it, the sword is from a time when Norse armour had lightened up a bit. So, I’m probably off base... But it makes me wonder.

Greetings Joseph C., While we are speculating, you may not be so off base. This may be a surviving custom job. I used to work with a guy that was just big and strong naturally. He was maybe 5'8" or 5'9". It was scary just to watch him take a deep breath. He called himself "Mutant" with great pride. So if you were this guy in Norse times with money or maybe a king with this guy in your service, that may be how this weapon came about. I have also read more than once that the Viking style of sword play preffered well timed blows with great force. Sincerely, Patrick Fitzmartin

A few of Bartas' other vikings are heavy also. Remember that these swords were made for the steel-thewed northern barbarians, not modern hobbyists.