The Aztecs demanded that a tribute in goods be paid to them, after they conquered a specific land. As long as the tribute was paid (which ensured their financial position), it was beneficial for them if the conquered people didn't revolt (too much), and if they didn't need to extend funds and infrastructure to govern them- that way they could pay little and maximize their gain. It was practical to reinstall the old rulers in the conquered lands, if they were sure of their loyalty, as it would minimize conflict and need for intervention (such as sending a lot of people into the new land) and maximize their profit.