What a second weapon can offer you, using only basic rules, is a second parry.
If you're highly skilled with a weapon type, let's say Rapier, then you will have a high Parry score with that weapon. Parrying twice with the same weapon is at -4(-2 for fencing weapons like the rapier) and therefore usually a terrible(fairly bad) idea, but with a second weapon you can parry a second time at no penalty*! This is useful against multiple enemies, in particular.
What All-Out Defense allows you to do, is to apply two defenses against the same attack.
In non-basic rules there are more things, like a Dual-Weapon Attack or Cross-Parrying.
It doesn't really benefit your offense, which is realistic, but it does help your defense.
*With Ambidexterity. Otherwise -2 for off-hand parrying.
Edit: After seeing your edit, I want to add that this will not cost you a lot more points. Ambidexterity is useful for all kinds of stuff, and this way you'll likely need to keep up one less skill...