Couple things- The majority of North Indians are dark skinned and short with the exceptions of a handful of castes, it's not black and white between the two (literally). Indian genetic makeup can be summarized as largely Iranic agriculturalists (non-Aryan caucasoids, ANE descent) who had dispersed throughout the subcontinent and mixed with coastal blacks who had migrated from Africa to Asia much earlier. Aryans mixed with this population as they invaded but their genetic impact is more significant in a small handful of high ranking caste groups.

As for the higher development of South India it's not because it's more or less black, it's that their lower castes (which make up the vast majority of the population) are significantly higher IQ than the lower castes of the north. So even if the north has more Aryan DNA (still a tiny amount), the IQ is what drives differences here.