Actually the typical broad sword weighed less, was shorter, and had a wider blade then the typical long sword.. While the (long sword a.k.a bastard)was designed to provide the 2 handed option for more power.
below are common statistic about each blade.
I believe the swords in game are based on these..
The Medieval Broadsword ranged from 30 - 45 inches, weighed between 3 - 5 pounds, and had a two-edged blade measuring 2-3 inches wide at the base which tapered to a point.
The Medieval Long Sword sword ranged from 40 - 48 inches, weighed between 5 - 8 pounds, and handle that measured 10 - 15 inches in additional length.
(mind you different area's and era's had variations on both let alone the fact that each smith or sword owner may have used modifications...)