Could improper installation of a weather vane on the roof cause a collapse?
Someone is being very paranoid!!! There's ABSOLUTELY no way the structural integrity of the roof has been compromised by installing a weather vane.

Edit:
Something else to consider about your daughters worries about the structural stability of the roof... Someone had to physically get on that roof to install your weather vane. If the roof was unstable, there wouldn't be a weather vane there as the roof would've collapsed under the weight of the person that installed it.