While that is true I think people tend to think of weight as the net downward force you apply to the surface of the earth, or basically, what the scale says when you stand on it. If you think of it that way, the balloon has a negative weight. If by weight you mean the force of gravity between the balloon and the earth, then you have a very different picture. Also, negative mass would create negative weight because it would be repelled by positive mass (supposedly, if it weren't, why would the mass be negative?).