Nope. Last time I went through weights and dimensions of actual historical ones, euros were still lighter. But depending on what lists of weights you cite, it’s barely noticeable, or more like a draw.
Thing is, a single handed european sword on average is a bit shorter than a Katana, so it is no surprise it is lighter.
But, the katana is a weapon with a long handle, that is usually used with two hands, but can for some purposes be used single handedly.
The equivalent to that in europe, would be the archetypical longsword, or sword of a hand-and-a-half.
European longswords tend to be a little bit longer than katana, BUT on average are still about equal in weight.
Basically, the weight of swords comes down to human anatomy and biomechanics, and a certain weight range overall has proven itself to be usefull for swords for human use, likewise some vague ideas of length of certain categories of swords.
But there is some influence of the materials available. And the japanese had the bad luck of being stuck on an island with very poor quality ore. The much fames folding of the japanese steel was not thousenfold to make it magically strong, but instead a few dozen times at best, to work out impurities.
Getting decent steel was extremely difficult in japan, and so they stuck to complex build ups of blades of diffrent sorts of steel, to not waste the very precious good steel. Also, the particular resources available meant they could harden their quality steel, but it tended to be brittle.
So as to be economic with the good steel and to have blade that would not easily shatter or break, they put together soft iron spine and an edge of steel, with the very edge only being differentially hardened.
Partially because of this, they ended up with a blade that does not have too dramati distal taper and is relatively thick still near the point. And thick means heavy.
Not dramatically, but a little bit.
The europeans had the luck of sitting on rather decent ore and by the high medieval times had figured out the production of reasonably good steel. steel, that would not only not tend to become brittle when hardened, but was relatively affordable. So they just made the whole blade out of the very same steel, and hardened and quenched the whole darn sword. The complete thing was, if all went right, essentially a spring.
The hardness was not as high as the edge of a typical katana, so edge retention during use usually was better with a katana, but a flexible mono-steel blade of springsteel neither was as suceptible to bits of the very edge craching and shattering away, nor to bending the blade, as the soft-spined katanas of hist. construction were liable to do, if a cut went wrong.
And as a bonus of that, the europeans managed to get away with slightly longer blades.
Sadly enough, though, many cheap replicas of swords are just plainly too heavy nowadays.
RPG and book authors etc havent helped by throwing around bullocks weight etc.
Basically, smiths in diffrent parts of the world used incredible skill to make the best weapons they could out of the materials available, and some mighty fine weapons they made. their cultures and the specific needs and goals lead to the weapons being diffrent.
But the idea of the european sword being a bruteish, heavy club, is wrong.