As a PA native I'm always saddened when the Commonwealth gets the short end of the stick in these "No Constitution = No United States" timelines. While this assumption is possible its not as likely as you may think. Until the completion of the Erie Canal in 1825, Pittsburgh was the gateway to the west. So long as PA keeps Pittsburgh the settlers moving in to the Ohio River Valley will in large part have come by way of PA.
This may not ensure that the Northwest remained loyal to PA but it will mean that the people living in the Appalachians and Ohio River Valley have little loyalty to the plantation society of the south eastern seaboard (case in point...West Virginia in our timeline). Given that without a central government the Pennamite Wars will be a bit worse and also given that PA is almost guaranteed to win (demographics and geography both work to help PA) we can assume that PA will occupy the Western Reserve claimed by Connecticut. Without the "Erie Chimney" PA will need this territory to give them access to the Great Lakes. So with access to both the Ohio and the Great Lakes PA will be in a good position to dominate settlement of OTL states of Ohio, West Virginia, Indiana and perhaps further west.
This leaves the possibility of two future conflicts over the old Northwest. New York is in a good position to settle the upper Northwest and will probably reach an agreement with PA. Once the Erie Canal is completed, which may take longer given the lack of a central government, settlement along the Great Lakes will once again favor New York. Further south the Pennsylvania / Virginia disagreement will most likely get worse. Washington and Franklin almost certainly will try to find a negotiated settlement, but once they pass on the final bonds that prevent war will be gone. By 1800, a year after Washington's death (though admittedly he may have lived a bit longer in this TL), Pennsylvania and Virginia will face off over the Ohio River Valley.
Assuming equality in military leadership, the war will come down to a contest of population and industry. Virginia has a lead in population but PA has more industry. If we assume that PA is allied to NJ (which I could easily be split along the old East / West Jersey lines and divided between PA and NY), MD and DE than the advantage would go to PA, especially if many of the settlers in western Virginia feel no loyalty to Virginia. Most likely the border would be set along the Ohio River. This would mean PA could easily extend to the Mississippi. Together NY and PA could easily purchase the Louisiana Territory and peacefully divide the regio allowing the river to remain an open international water way and New Orleans as a free city.
Just my thoughts on the matter.
Benjamib