Where did you get that southern Germans were bigger supporters of unification? The Bavarians liked the federation that ws the Holy Roman (german) empire — and they like the Federal republic of Germany today which gives a lot of power to the states. The southern germans did not want unification under the Prussians — the Prussian warlike and anti-Catholic culture is what defines the current German stereotype
Decades later, most of the National Socialist leadership came from southern Germany (Bavaria and Swabia). They certainly didn’t oppose unification.