AHC/WI: Frederick Barbarossa gives the Duchy of Saxony to a Hohenstaufen or an ally?

In OTL, Barbarossa divided Saxony in 1182-1185 into many states after confiscating both the Duchies of Saxony and Bavaria from his cousin, Henry the Lion of House Welf, 2 years earlier. Bavaria was given in its entirety to the House of Wittelsbach, beginning their long reign over Bavaria that would last until 1918.

Saxony was divided amongst the nobles who had supported Barbarossa against Henry the Lion. How could it come to be that Barbarossa instead gives the entirety of Saxony to one ally, as he did with Bavaria, or even gives it to another member of his own family? What would be the consequences of doing so?

Actually Bavaria wasn't given in its' entirety to the house of Wittelsbach. After the march of Austria was split from Bavaria and raised to the duchy of Austria in 1156, in 1180 the march of Styria was split from Bavaria and also raised to a duchy.
Also the house of Andechs, which held extensive lands in Bavaria was granted the duchy of Merania.

So what Barbarossa did in Saxony isn't too different from Bavaria, and IMHO appears to have been a deliberate policy.