Shinra launched a rocket at Meteor. Magically, it pulled itself together. The only materia that could harm Meteor is the white materia, Holy.

Also, I've said it before, Jenova was the behind-the-scenes bad person. Jenova just moving around the Planet again is not enough to call the Weapons, as she was out and about for all of Disc 1. Sephiroth was not a threat enough to the Planet either. However, Meteor had the capability of damaging or destroying the Planet, so it endangered the Planet itself, not just the life on it. So the Weapons came out of their sleep. They might not have even known what the threat is, just that they have to destroy everything until they find the threat.

Plus, if you don't believe this explanation, what reason can you give for the Weapons acting as they do?