Albert Barnes Commentary Numbers 32:33

"And Moses gave unto them, even to the children of Gad, and to the children of Reuben, and unto the half-tribe of Manasseh the son of Joseph, the kingdom of Sihon king of the Amorites, and the kingdom of Og king of Bashan, the land, according to the cities thereof with [their] borders, even the cities of the land round about." — Numbers 32:33 (ASV)

Half the tribe of Manasseh - That is (Joshua 17:1), the families of Machir. Moses, when assigning to the pastoral tribes the inheritance which they desired, appropriated to these Manassites especially the district they had already subdued, as a reward for their valor and exploits. Thus, the whole of the conquered country was provisionally disposed of, and the initiative and valor of the Machirites rewarded. It seems clear from Numbers 32:39 and Joshua 17:1, that the claims of the Machirites arose simply out of their exploits.