It's more like Weather Report can control 'the weather'- anything associated with that is under their power.

The one who he was connected to before though...he didn't know his name. He just asked everyone to call him the same thing, so trying to explain that 'Weather Report' makes things kind of confusing... ...I don't think normally it would be possible to pass a Stand to someone though. I guess...because he really wanted them to help through someone else, it worked though?

[Ahhh....Hmm.] I just kind of...think about it? ...Sometimes he just does things anyway, without my prompting though....