swordplay is fast, but the movement is completely different than running around.

quite true. there its about offensive / defensive positioning, and maneuvering for advantage. its only when you run away that you want to sheath your blade for maximum speed. and then its not due to the weight - after all , you're still carrying it - its due to the awkwardness of carrying it in your hands while fleeing. i suspect that in general, without a large weight in one's hands, one is better balanced for running fast. it definitely requires more energy to run with a weight swinging at the end of your arm. get a pair of dumbbells. go outside. now try to run with them in your hands. now tie them to your belt and try to run. big difference - same weight.

BTW, did you ever hear of the tabletop rpg called "privateer" (or was it musketeer?). it was a 3 musketeers rpg, with emphasis on sword dueling combat, and gaining social prestige.