Long post coming up 
Development is no exact science. One of the reasons a big city does not always mean as high development as another is that urban population in this era was so sensitive.
This is especially true for the capitals of great empires. From your examples both Tenochtitlan but especially Cusco (which was nothing special at all in 1444 from what we know) likely attained their sizes in the period between game start and 1500. When the Mughal capital is moved to Lahore the city is estimated to have grown by more than 200 000 in just a few years, only to loose that population again when the capital was moved away.
Likewise things like war and disease can decimate a city in just a few months (Vijayanagar is a good example shrinking to around 50 000 quickly after the battle of Talikota).
When dishing out development things like the population of the entire province, density and durability of urban concentrations as well as (when available) actual information about what income a state in the area could get from that part of their lands. While it is often true that a capital would be situated in a wealthy region we prefer not to make a region wealthy just because there was a big capital there (after all the capital may not remain in the game).
Of course often we have to base of these things on pretty shaky figures in the first place as knowledge of historical demographics is often not that good for many regions (there are for instance no written sources of inca history prior to the arrival of the Spanish, so all we know is deduced from what people could remember at that time + archeology).
To continue with the Vijayanagar example: The coastal Tamil lands where extremely fertile and densely populated and housed many thriving cities with strong and old merchant communities. The city of victory itself was huge and the land it occupied was nothing to spit at, but when it came to economics the Vijayanagara rulers trusted the southern lands to feed the city, the city itself was not a major production hub or source of tax income. Indeed in the end what happened was the outlying regions deciding they had no use for the center and the city shrunk rapidly as It no longer functioned as the capital of all of southern India.
That said perhaps there are some of these regions that could do with a boost. I just want to object to big city = rich province.
Development is no exact science. One of the reasons a big city does not always mean as high development as another is that urban population in this era was so sensitive.
This is especially true for the capitals of great empires. From your examples both Tenochtitlan but especially Cusco (which was nothing special at all in 1444 from what we know) likely attained their sizes in the period between game start and 1500. When the Mughal capital is moved to Lahore the city is estimated to have grown by more than 200 000 in just a few years, only to loose that population again when the capital was moved away.
Likewise things like war and disease can decimate a city in just a few months (Vijayanagar is a good example shrinking to around 50 000 quickly after the battle of Talikota).
When dishing out development things like the population of the entire province, density and durability of urban concentrations as well as (when available) actual information about what income a state in the area could get from that part of their lands. While it is often true that a capital would be situated in a wealthy region we prefer not to make a region wealthy just because there was a big capital there (after all the capital may not remain in the game).
Of course often we have to base of these things on pretty shaky figures in the first place as knowledge of historical demographics is often not that good for many regions (there are for instance no written sources of inca history prior to the arrival of the Spanish, so all we know is deduced from what people could remember at that time + archeology).
To continue with the Vijayanagar example: The coastal Tamil lands where extremely fertile and densely populated and housed many thriving cities with strong and old merchant communities. The city of victory itself was huge and the land it occupied was nothing to spit at, but when it came to economics the Vijayanagara rulers trusted the southern lands to feed the city, the city itself was not a major production hub or source of tax income. Indeed in the end what happened was the outlying regions deciding they had no use for the center and the city shrunk rapidly as It no longer functioned as the capital of all of southern India.
That said perhaps there are some of these regions that could do with a boost. I just want to object to big city = rich province.
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