In the Skyrim discussion board there's a discussion about the weight of swords and how it affects combat:
http://www.gamesas.com/index.php?/topic/1167757-swords-are-not-heavy/
In a nutshell, the OP believes the medieval swords are not heavy, but some folks think the weight posted by the OP will not be enough to induce high damage, which is also not effective to block.
The discussion is getting heated so I don't see a chance for myself to post my opinion, so I moved to here

Swords are not designed to hack. Depending on the shape of the sword, it's best either for thrusting or slicing. Think of human flesh as a tomato. Have you ever tried to cut a tomato? If you have, you probably know that if you try to press the knife down on the tomato, the skin will just sink down but won't yield. The only way you can defeat a tomato skin is either stab it with the tip of your knife, or use the "slicing" motion. An extreme to thrusting is a rapier, while an extreme to slicing is a japanese katana, both look rather too fragile to hack like an ax. In either way of using a sword, weight does not matter, but rather agility and speed in order to repeat the slicing and thrusting motion precisely and quickly.
Thus comes the "balanced" part of sword quality. The pommel of a sword is used to counter the weight of the blade, and makes repositioning the sword for the next attack an easy task.
To block a blow with a sword, likewise, is not depending on the weight of the sword. When you block with a sword, you aren't really trying to stop the motion of the enemy's weapon. Your goal is to change the direction of the enemy's blow, which if done correctly, requires very little force to accomplish. Think of when an object comes at you in the X direction. Instead of trying to stop it, you give it a force towards the Y direction, thus the object won't hit you while it continues on its motion. It's a subtle and challenging task and only the fighter himself knows how it works, while bystanders like us can't really see what's going on.
Swords ARE designed to hack, slice and stab. 'Hacking' is the fastest and most effective offensive movement your arm can produce. Early forms of the sword, the Egyptian kopesh, the Iberian falcata and the Greek kopis favoured the use of hacking blows. Strikes , however, do not need to piece the skin, a blow to the side of your head will concuss, bones will break and muscles will be crushed. The whole point of fighting is to make the other person stop moving in a defensive manner. An immobile warrior is a dead warrior. Stabbing will pierce armour much easier than hacking or slicing, which is why a stabbing weapons was a favourite for the Romans with their gladii, Greeks with their xiphos and the seax with other Dark Age societies like the Saxons and Vikings. But outside of their formations, a warrior depended on his sword to both stab, hack and slice - which is why it remained in such high popularity throughout the ages. A sword's versatility was its main selling point and to say that hacking was not one of its primary design functions would be grossly inaccurate.
Your tomato anology is good if you're just looking to cut down unarmoured opponents but most people weren't foolish enough to wander into battle without some form of protection. To say that human skin is like the skin of a tomato is not an apt comparison, human skin is much more pliable. The skin of a tomato should instead be likened to a lightly padded jacket or boiled leather (cuir bouilli) - a stab will get though easily enough and a slice with a sharp enough knife will cut through it cleanly enough but that's not the objective. You don't particularly care about nice clean cuts, you just want that armoured guy to stop flailing his sword around so you can go home to your wife and kids. A hacking blow might not get through his armour but why go for a killing body shot when you can just disable him? Many Migration Period graves proves this, most of the injuries are to the head (concussion), to the legs (crippling/hamstringing) or to their arms (disabling). A warrior that cannot fight may just as well be dead.
Using rapiers and the Japanese katana as your examples is a bit of misnomer. The rapier came about as gunpowder became more prevalent and thus the use of armour was in decline.Thrusts will skid off armour, find chinks between plates and pierce through jerkins. That's why the rapier was designed the way iit was. If you jump back about a hundred years, the estoc or tuck was a needle thin longsword that was designed especially to defeat armour. As for the katana, it is the quintessential cutter. Japanese swordsmanship emphasised precise cuts to exposed junctions in the armour, forgoing the armour piercing debate altogether. When the Portuguese imported maille, sword morphology changed and they developed, for a time, katanas with spear pointed tips. But to say the katana was only good in slicing is just plain wrong. The thrust was important, it might not have been as important as cutting but the ability to thrust still existed. In fact, the only time a sword was designed with the inability to both thrust and cut were the execution swords used only for beheading of criminals.
The use of the pommel as a counter-weight is largely only applicable to early modern period dueling weapons and retroactively applied to medieval and dark age swords during the era of Victorian revival. The pommel was originally intended to stop the users' hand from slipping off the grip - its use as a counter weight was merely incidental. If it was really meant to be used as a counter weight, it would have to be quite a few magnitudes larger and heavier.
Your notion of setting aside the blade instead of blocking is good - this is known as 'Absetzen' in the german school of swordplay. But solid blocking parries do exist and when fighting with swords of mismatched weights, it is always easier for the light-blade to block than to set aside a heavier one. Setting aside a large heavy blade will be like trying to ram an F150 off the road with your Mini Cooper.