Pretty much any scenario could happen, and balkanization in the early 1800's is a very different beast from the late 1800's.
In 1800, Virginia is the most populous state (807,557), with very high chances of expansion into the currently "territory" of the Great Lakes Region. Given it's political power at the time, it's not impossible to see it expand well and keep on growing. However, the large slave population and the slower population growth it saw OTL may make this hard (by 1900, Virginia + West Virginia would have been the 7th most populous state at around 2.8m).
Pennsylvania was the second most populous state in 1800 (602,545), and remained the second most populous one throughout the entire century (reaching 6,302,115 in 1900). It was similarly well placed for good expansion into the Great Lakes, and probably has better long term industrial prospects that Virginia, but it suffers from lacking coastal access, which would be especially damaging as an independent nation (meaning it would have no independent access to world trade and migrants, which could massively cut its potential.) It is also right inbetween two populous neighbours that - if relations turn sour - could well decide to "claim" some of its land.
New York had become the most populous state by 1810 (959,049) and stayed like that throughout the century (7,268,894 in 1900). It has the advantage of having a great port city (NYC) that would have been prime for immigration in favourable circumstances, thus giving it an advantage in growth, and it already had a great industrial base. It's disadvantage is that same city however, located in a horrible strategic location if there were ever any conflict between it and neighbours. It is also "hemmed in" by other states and by Canada; meaning it has to resort to force or to some form of micro-federalization in order to expand. *if* it achieves either successfully (whether to the north forming a "Greater New England", or to the south/west taking Penn land), it becomes the undisputed hegemon of the early century.
These three states (or any combination of them) are the main contenders for the early part of the century, and it comes down to who is able to expand into Ohio and the great lakes.
Take it to late-century however, and it becomes a very different beast.
The northern/great lakes states are still the most populous, but cannot really "expand" territorially, having to rely on growth within their borders instead. Whoever manages to create some sort of "federation" of a region of states will most likely win. If nobody makes a federation, NY/Penn/Ohio/Illinois stand the best chance, remaining prosperous immigration magnets from Europe that can keep growing in population until they reach European density levels. NY still has the advantage of NYC and direct access to the sea.
Texas and California are still pretty bare on population, and without being part of the United States would be less attractive as destinations for immigration (though they would still see some; Texas more than California due to ease of access). It would likely be too late however to establish the necessary "base" to become a great power in the next century.