FWIW, Norman swords were very large, especially considering they were only used single-handed.
These are probably the toughest types of swords to use well. Huge learning curve + very strong grip required.
You are correct.
*Warning* Nerd post ahead !
Most swords roughly weighed 2,2 pounds. The most important factor was the point of balance ( the point on a sword where there is an equal weight distribution on both sides. It is measured from the guard.)
"Viking" swords were typically larger versions of Roman Spatas, which were "choppy" type swords as opposed to the "stabby" ones.
Earlier Scandinavian swords had heavier points whereas later swords had balance points closer to the guard when steel quality improved, around the 10-11th century ( for example :
Ulfberht produced swords made from pattern welded Damascus steel.)
The sword's hand became longer and the pommel slowly morphed into a "brazil nut" pommel type.
The Petersen Chronology and Classification of Swords gives you a good idea of how Viking sword designs evolved through time.

With that said, swords were hardly weapons of choice on the battlefield. Spears were MUCH more efficient.
During raids, the Vikings predominantly used Dane Axes.
No written accounts of Viking ( Scandinavian ) history ever existed, so it's hard to contextualize their warfare tactics and equipment.