Slagzwaard in Dutch means literally 'cutting sword'. According to the descriptions I read it was to heavy to be wielded with one hand or from horseback (you'd fall of your horse). It should be wielded with two hands. Maybe this description refers to the times when everyone considered Medieval swords as too heavy to even lift them. There's also a reference to executioner's swords. Am I correct in supposing 'slagzwaard' refers to XIIa and XIIIa swords like the Baron, the Duke etc. On the site where I found this information there's also talk about a 'boorzwaard', literally 'drilling sword'. This type is clearly described as evenly tapering towards a sharp point and to be used for thrusting (drilling) into the slits of armour. A 'boorzwaard' is considered a later evolution than a 'slagzwaard'.

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The term covers the great slashing swords of the high middle ages (but is adopted into later periods as well). The types XIIa and XIIIa would be perfect examples, but also XIII, heavier XVIa, XVII and XIX or for that matter XX and XXII.
If you call them heavy or not is very much a matter of what you compare to and what you expect. They *are* massive in weight, compared to many single hand swords both from the medieval period and later, but they are still balanced in a way that they can be considered agile (more agile than some later period military sabres and pallasches). Long blades and large mass will have an effect on how you perceive them of course. I prefer to describe them "massive and well balanced", rather than "heavy and large", even if they truthfully fit both descriptions. To someone who is not experienced with the traditional shapes of the european sword, the word "heavy" can be very misleading, as it evokes notions of clumsiness. Therefore it is rather popular to underline the agility and responsiveness of these swords when we talk about them among ourselves in places like this forum and "preach to the masses" when we do public demonstrations. They *are* pretty massive, however. Let´s not forget that.
They do come in slightly different size. Some are too big to be effectively wielded with one hand only. They are two hand weapons. Some can be used with one hand if you have the physique and training to carry this through. Some are bordering towards "bastard swords" in that they can be used almost equally well with one or two hands. I am not sure these lighter and smaller ones are accepted as "Slagzwaard" however. I guess that ultimately depends on who is writing the text. Personally I think even the smaller ones were made especially for war, and so classify.

In german the word is Schlachtschwert (spelling?). It is not slaughter, but battle (even if those two activities can be much the same at times). So Battle Sword, or War Sword is another name for these weapons. Personally I think that is a pretty good name, as it rather well evokes what it is all about: making an impression on opponents on the field of battle. Several different designs are useful here, that can be described by the same word. The history of the sword is seldom very exact, especially when it comes to naming of types. So if we accept the name Battle Sword as a useful definition for a group of weapons, we can then look at surviving swords and see which of those would fit the bill and get the job done. They tend to be sturdy and rather largish. They are often strong cutting swords capable of delivering powerful blows. Being swords, they cannot be clumsy or they would not be effective weapons in the first place, but they are not fencing foils either. Knowing the array of armaments available to warriors at the time, we can conclude that swords must be able to pulp muscles and crush bones, when armour makes an effective cut impossible. Therefore size and mass is as important as agility and cutting ability: hence the design. Please note: I am not saying they were not sharp, but that they are capable both of powerful impact blows, as well as devastating cutting depending on the situation. (And of course there are often areas that are not so well covered by armour: a cut here will easily be devastating.)

Boorzwaard, is a term used mostly for those later specialized forms of thrusting swords, (I think mostly in two hand or hand and half size, even though you see exactly the same type of blades for single hand use as well). This is the other option, when you face difficult targets in hard shells. The classic types belong to the late 15th C up to mid 16th C. Functionally you do see very narrow, very stiff and impressively long blades much earlier. There are long swords and single handers that fit this description already in the mid 14th C. They are commonly called thrusting swords, however.
Estoc is another name for the general type and that term see a wider application over varying shapes and configurations.

I think that the Oakeshott XIIIa would be an example of the former type. It seems to have the longer blade of that type (one listed was forty inches) and a 6-8 inch long grip. These swords are a little longer for use from horseback with a little more weight to give more power to the blow. The latter would be something like the type XVII which Oakeshott describes as a heavy pointed bar of iron, at least the specimen he once owned. The blade was narrow, sharply pointed, very stout, hexangonal in cross section, and having a hand-and-a-half grip.

As Peter said, heavy is a relative term. A sword so heavy that it could unbalance the rider and cause him to fall from his horse would have been worse than useless. I would hazard a guess that the heaviest of the type XIIIa's would probably run around 4 1/2 pounds. A sword has to be light enough that it can be wielded, at least intermittently, for hours. There was no calling for a break to catch one's breath.