KarinsDad said:
I'm basing that idea on the fact that it is the rules.
Nothing in the Invisibility spell explicitly states that the creature sees himself.
Hence, he does not.
The Invisibility spell states that a creature is Invisible. Hence, he is Invisible to everyone (including himself) unless someone (again, including himself) has a way to see him.
For your assumption to be true, the rules do not have to state that he explicitly cannot see himself, they have to state that he explicitly can see himself. The reason is that the rules already state that if he is Invisible, he cannot be seen. That is the default rule. Hence, the burden of rules proof is on someone who claims (like yourself) that he can see himself.
I agree with Karinsdad, and his original post was the most insightful.
I tend to agree with the idea that in a melee fight, a fighter wouldn't be terribly hampered by an invisible weapon. I think the concept that "this sword is just an extention of me..." is more than a cliche'.
In baseball, do you look at your bat when you swing? Same concept. Keep your eye on the ball. Focus on your target.
Also consider that when you watch chinese martial arts you may notice some of the weapons have rather elaborate tassels attatched to the spears. This is designed to distract their opponent (who IS looking at their weapon); yet, because of their training with their own weapon, they do not distract themselves. Again, they don't look at their own weapon, they look at their opponent's.
So what kind of bonus should be given? Well, IIRC, and I don't have my PHB at hand, being invisible gives you a +2 to your hit. Having just your weapon be invisible isn't nearly as good as that, so halve it, or deny dex bonuses, or both, whatever works balance-wise...
I don't know if this qualifies as proof,