Weapon weight is a factor in some situations(warrior skill weaponbreaker(heavy axes break enemy weapon easier) and warrior legacy trapping beneath thunder), but I don't the weapon weight affects the fighting capabilities(parrying/dodging the weapon). Heavy weapons are dropped easier than light ones when you are maledicted and are not strong enough to wield it(your strength determines how heavy weapon you can wield). When wielding two weapons, the heavier one will always go to your main hand and the lighter one to offhand. Also, your dodge skill will be affected by the total weight you carry.