Any of you guys ever had a sword in your hand?
Ofcourse it's possible to jump with a sword and it's also possible to swing, but you hardly do any damage or whatever with it and you hardly block and the possibility that you stumble because of the weight affecting your jump is very high.
We are talking about european swords, not about asian sabres 
Yes, I have held a sword that isn't a cheap piece of replica shit that weighs more than a real, balanced sword. Even the biggest european swords only weighed about 8lbs, wielded with two hands by someone who has trained for year after year with it, it isn't going to feel heavy at all. And 8lbs is the most extreme,alot of the larger two handed swords weighed between 4-6lbs.
It isn't going to effect your jumping at all, but I don't really see the issue here, jumping ingame in a melee battle results in death most of the time unless you are fighting an unskilled opponent, anyone with an ounce of skill will easily defend or counter such stupid attacks. Where as jump shooting with a bow was beyond ridiculous and allowed infinite kiting, it is much more believeable to jump and swing with a sword than it is to jump, knock an arrow, pull back bowstring and fire upon landing.
Also, recently watched an excellent documentary where they demonstrated alot of stuff, like a guy in a 40lb suit of full plate armour made to fit him, was running across a field with a sword at a decent pace, was very agile and could easily run up to and mount his own horse.
