I wouldn't use the term state since it implies a degree of geographic expansion that probably wasn't present. Most polities in the region were city-states. Some had established relations of dominance over some of their neighbors but those relations were necessarily modeled along 'state' lines.

To answer the specific question the two biggest regional powers would have been Azcapotzalco and Texcoco. Eventually, the Mexica would ally with Texcoco and Tlacopan to over throw the regional hegemony of Azcapotzalco.

Here are some readings that might help:

Blanton, Richard, and Gary Feinman. "The Mesoamerican World System." American Antiquity 86 (1984): 673-82.

Carrasco, Pedro. "The peoples of central Mexico and their historical traditions." In Archaeology of Northern Mesoamerica, Part Two, edited by Gordon F. Ekholm and Ignacio Bernal. Handbook of Middle American Indians, 459-73. Austin, TX: University of Texas Press, 1971.

Davies, Nigel. The Aztec Empire: The Toltec Resurgence. Norman: University of Oklahoma Press, 1987.

Hassig, Ross. Aztec Warfare: Imperial Expansion and Political Control. Norman: University of Oklahoma Press, 1988.

Smith, Michael E., and Frances F. Berdan, eds. The Postclassic Mesoamerican World. Salt Lake City: University of Utah Press, 2003.