When I've experienced more of the kinds of weather, I'll be able to answer it. So far, because it's Winter here, I've had:
1) Partly Cloudy
2) Snowy
3) EXTREME WEATHER
4) EXTREME WEATHER
5) EXTREME WEATHER
6) EXTREME WEATHER
7) Windy
So far, Partly Cloudy and Windy have had the best results for me. A level 35 Ralts, a bunch of Level 35 Weedles and some Level 32+ Pidgeys, a Ditto and others. And more Ralts (caught 2, hatched 2 - both 10km eggs I've gotten since the new Weather system have been Ralts) and Makuhita (seen 4, caught 4 with Pinaps) than I expected.