Their squabbles are frequent, but never do they flare to continental war. Pennsylvania is still the most powerful nation, though it speaks a different language by majority. Virginia is powerful as well, but there are lingering racial tensions between the descendents of slaves manumitted in the 1900s, the old planter aristocrats and the middle class farmers.
There are smaller states with little to no military power beyond the Appalachians, such as the Watauga Association, the Ozark Republic, and Ohio, but these are dominated by the Republique d'Lousiane and the merchant elite in New Orleans, though since the native revolts in the northern prefectures, they have moved away from Lousianian dominance.
Past that are Tejas, California, and other Spanish speaking states ruled by caudillos after breaking from Spain or Mexico.
The largest wars have been Virginia and Pennsylvania in the Wheeling War in 1920, a dispute over the town of Wheeling on their common border that lead to full scale warfare and the Virginian Army shelling Harrisburg and Pittsburgh until air raids on Richmond and Newport lead to a treaty.
Mostly these states occupy themselves with trade and their internal affairs. To Balkanise them would create a needless rival to the balance of power in Europe. Why does the world need yet another empire? Are we, in the United States of the Danube, whose democratic society replaced the oppression of the Hapsburg tyrants, not an example enough for humanity? These republics and petty states would better occupy themselves with emulating us rather than forming themselves into a competitor.