How were the USA's state capitals chosen? Clearly not by size or economic might e.g.NYC isn't the capital of New York state, and despite all the major cities in California, the capital is a place called Sacremento.

The city chosen to be capital for a given region may change from time to time, typically during rapid population growth or time of governmental instability caused by local war. When territories were divided up into smaller states, especially during the 19th century, new capitals within the new boundaries needed to be chosen.

These decisions are largely made by the Legislative branch of each state, though no changes have been made since 1910, Oklahoma City replaced Guthrie as the capital of the State of Oklahoma.

https://en.wikipedia.org/wiki/List_of_capitals_in_the_United_States#Former_state_capitals

New York City is not the capital of New York on account of the fact that in 1614 the first major settlements were constructed as Dutch forts in Fort Orange, a location nearby present-day Albany. Many capitals date back to early history like this.

Many capitals are chosen because they are in the center of the state, but each state has its own reason for choosing its capital.

Probably second behind New York, most people (even Americans) are surprised to learn that Baltimore is not the capital of Maryland.

And that Philadelphia is not the capital of Pennsylvania. In the cases of PA and NY, around the time the colonies had declared independence Philadelphia and NYC were the largest and most important cities in their respective states, but there were tensions between the people of Philly and NYC and the rural populations in the rest of the states, so their capitals were set in Harrisburg (PA) and Albany (NY). In Maryland, Baltimore did serve as the capital city for some time (as did Philadelphia), but during the Civil War Baltimore was heavily pro-Southern whereas most of the rest of the Marylanders were abolishionists, so the capital was changed then when the front got too close to the Pennsylvanian border.