No weather: Normal
Sun, extremely harsh sunlight: Fire
Rain, heavy rain: Water
Sandstorm: Rock
Hail: Ice
Shadowy aura (XD Gale of Darkness): Typeless
Ion Deluge and Electrify if there is no weather: Electric
In addition, despite being displayed as Breakneck Blitz and Max Strike, Weather Ball will become the same type as the current weather
Weather Ball is also affected by Aerilate, Pixilate, and Refrigerate, and will become a Flying/Fairy/Ice type move if there is no weather up (Thanks sumwun)
Source: Experience, and this