Hi - going to respectfully disagree. No need to believe what I say as there is lots if interesting info on the net if you want to learn more.
Rapiers were not lighter than one handed medieval swords. They weighed about the same. It was the weight distribution that was radically different with the weight of the rapier shifted towards the hilt. Rapiers were never meant to face armored opponents. Rapiers were personal arming swords and were not generally used on the battlefield. Not enough stopping power.
The two handers to which you refer would be more 15th/16th century weapons. They would be heavier (up to 7 lbs) and would be used for all sorts of things - against cavalry, a pike wall, etc. These were not medieval weapons.
Oh I don't claim to be an expert either

I picked up a katana once, and it was heavy. Took both hands to lift the blade. And I'm not weak. But that was a
katana, not a
long sword or
rapier, and it was a reproduction of a katana...the edge wasn't sharp. The blacksmith said that was the only difference...but he would wouldn't he? Some blacksmith at a fair. But, that is beside the point

What I've read before, as I stated, could be wrong. And I could have mis-read it. But here's the thing...
Have you ever picked up 1.5 meters of steel? It weighs ore than 3lbs

That is modern steel. Medieval steel is going to be heavier, and more brittle. I still believe the medieval swords were heavier than 3lbs

3lbs is really, very light. I believe that soldiers were just stronger then, because they were farmers and did nothing but physical labor all day long. And I also believe there wasn't any fance "sword play" in battles. I think most soldiers just ran up and started hacking at you with the blade. This is medieval Europe we're talking about. No Japan or China. There was no such things as "martial arts" in France or Italy or Germany. There were peasants who were given cheap swords, that broke easily at were often rusty besides.
The concept that is portrayed in nearly all the fiction that uses it, is that there were skilled swordsman. But this is a romance drawn from the modern romances of "martial arts" and the sport of
fencing which uses very light "weapons", that are more like gaming utensils. Tennis rackets. Hockey sticks. Golf clubs. Not in size or weight, but purpose. But fencing developed in the renaissance.
I'm saying iron is heavy. Steel is heavy. And suggesting that, while I'm sure some were better than others, and there was a concept of "best" swordsman, the kind of artistry displayed in fiction/film/video didn't really exist.