Rain
Sun (as in, get rid of clouds)
Wind
Snow
Hail
Clouds
Tornado
Lightning
And anything else I might have missed. Preferably, the weather machine should be based on the ground, but it doesn't have to be if your idea wouldn't work like that.
Personally, I can only think of ways of creating lightning, rain and sun. To create lightning, I would replicate what Tesla did at his base in Colorado Springs, (pulsing electricity through the Earth to make lightning arcs shoot out of a tesla coil) except I'd place the tesla coil up in the sky and point it down towards the ground.
To make rain, I would fire tiny particles at high speed into clouds, which the water vapour would condense onto and form water droplets.
To clear the clouds away to make it sunny, I would simply fire a high powered laser at the clouds to vaporise them (physics works like that, right?).
Anyway, how would you do it?