I've been away studying martial arts for my WIP for a while, but decided to drop in and see what's going on at the AW.
From what I've seen in martial arts, using your enemies weapon along with your own to bind their arm and take them down is a common and effective strategy. As is wrestling with them at their weapon.
Trying to engage an enemy with an off hand is difficult to do because of the coordination and strength differences between each hand. The average joe warrior won't be able to actively be attacking with each weapon. This makes his off hand a weakness when he attacks with it.
A skilled enemy would bind his off hand or use it to throw him down.
In the case of someone who is skilled at using two at the same time, there are some advantages, such as being able to keep the opponent guessing from which side the attack is coming from.
There are situation in which a second blade, even for a skilled user would just be something else sharp for them to fall down on.
Examples are German Martial arts favourite move of ringim am schwert. or wrestling at the sword. There were a couple of ways they could do this with your weapon.
One example, they would parry your blade, and then half hand their own, turn on yours and step behind you and bind their hilt across your chest. Pull and flip you onto the ground so hard you lost your weapon(s)
Another, they would parry your move out from you, step behind your leg, place their off hand across your chest and throw you to the ground.
Most of the moves I have seen in martial arts seem to make sure the dominant hand is made ineffective and the off hand can not reach you, while allowing you to use your off hand to attack.
This is the reason why smaller blades were normally used with a larger one. I can change a throw from placing my arm across your chest to placing my dagger in your armpit.
Another factor against a double weapon is a lethal engagement between two well trained combatants doesn't last the minutes of hollywood, the tens of seconds of fantasy. It lasts as long as a gun fight. 3 to 10 seconds. you likely would never get to even bring your second weapon to bear.
To summarise my lengthy rambles. A second weapon has some advantages but they are nominal at best. unless the second is small enough to be used in throws against an enemy, but not long enough to be used in throws and binds against you.
I'll finish this post with a pair of youtube videos, showing how quick a real encounter lasts. and some of the moves mentioned above.
Long Sword Technique
Ringen am Schwert