Lighter swords with huge mass

Lets suppose we have a material that is not equal affected by gravity as everything else,I don't care how, anything from dark matter to fairy dust works, but the point is that the weight formula for this material is

w = m * g * d

Being d a value between -1 and +1

This material has mor or less the same properties as iron and alloys are posible, so you can make a "steel" sword.(When alloying lets suppose d do not change)

Now we have four different materials:

The first one(A) has all iron/steel properties but d=0.5

The second(B) is 10 times dense so ten times mass and is of course has ten times toughness, hardness etc... (and yes It can be work in a forge because of the fairy thing)in this case d=0.05

The third(C) is the same 100 times everything d=0.005

The forth(D) ... d=0.0005

Time to swing that swords! But, what will happen?

Test 1

Broadsword made of material A 1m long 1700g*0.5=850g

I'ts a light sword but when you swing it feels somehow heavy.

Test 2

Same sword but made of material C I'ts a light sword but when you swing it it feels very heavy, hit like a truck and if not hit anything maybe trough you to the floor.(Please grip it well or it will hurt someone)

Test 3

Same sword but made of material C

Here I suppose that you barely can move the sword

Test 4

Same sword material D but you have super strength(balanced whit the sword mass) but with the average human weight

So you are swinging the equivalent of a truck (And this literally hit like a truck)

Finally here are the questions:

Can you explain what will happen in Test 4? Will you fly away?

In addition

If g is gravity acceleration, anything made of this material should fall at d times speed right?Then, there is a logical way to implement this with the same falling speed? Like(I hope this is clear enough )

w = (m * g )* d (forget about math rules here just focus on the idea)

Feel free to point any unsuspected behave in the other test or even make extra ones if you like(This is not required for the answer as it may be considered too abroad)