I'm not a historian and I'm not exactly sure how to ask this question. I understand that during the Age of Discovery the typical process of a European power making a territorial claim in North America involved (1) sending an explorer across the ocean on a ship (2) planting a flag and claiming a parcel of land for a particular empire (3) defending the territory against rival claims particularly in war. For an island, this is relatively straight forward: land on Hispaniola, plant a Castillian flag, build fortifications and settlements, and defend the island from English or Portuguese attack. But on the land mass of the continent itself, it appears that history followed a different course. Here territorial claims often appear to be made by drainage zone. For example, French Louisiana was the the Missouri/Mississippi drainage area. Rupert's Land was the Hudson Bay drainage area. Possibly (I'm not sure) the St. Laurence and Hudson River Drainage played a role in territorial claims for New France and New Netherlands, respectively. Why were watersheds so important in defining territorial claims? How could England claim Rupert's land as far west as the Rocky Mountains before setting foot within 1000km of this western limit? Did these claims tend to be respected internationally? Why did the European powers not make bolder claims to the entire North American continent? Why did France not recognize the Vatican brokered Treaty of Tordesillas that would have granted much of North America to Spain?
The essential problem was how a monarch, living thousands of miles away from a continent, could grant someone a big piece of it when none of it had been surveyed. Defining that territory in terms of rivers and tributaries made that somewhat simpler- there was no doubt as to where the route of a river ran. Rivers were also immensely important. For the early colonists along the Atlantic coast, the rivers offered the best means of transportation. River bottomland was the best for agriculture, making them very important for an economy almost entirely based on farming. It is not surprising that settlement tended to follow the rivers. A plantation in Virginia would be set on a river, if possible. Growing a tobacco crop was far more easily done on bottomland , and the harvest far easier to ship off on boats than on wagons, even when there was a decent road available (and in the early colonies, there usually was not). A river also provided a source of water. Even today, a large city that is not on a river is a rarity, and still can have problems. Atlanta, in Georgia, has been cursed with having unreliable or insufficient water supplies almost since it was only a railroad junction.
The claims based on a rivers logically had to include a reference to the headwaters of that river. This became a problem for many colonies, as that can be rather subjective. Maryland's 1632 charter, given by Charles I, defined its southern boundary as the Potomac river, extending to the "first fountain". Charles II would grant another charter to the Culpeper family in 1649, for what was called the Northern Neck, that stretched south from the Potomac and also extended to the headwaters. But for decades, no one really established where the headwaters of the Potomac was. The Northern Neck then became a problem for the Virginia governors. The Northern Neck's owner, Lord Fairfax, living in England, was content to allow squatters to settle in it, but would not actually sell or grant land in it. Annoyed by this, and afraid that unless the land was settled there might be encroachment by the French, Governor Gooch defined the headwaters as being pretty far east , where the Shenandoah and Potomac Rivers met at what's now Harper's Ferry. Then he began to grant land north and west of there. This created a dispute with Fairfax, who moved to Virginia in 1735 to settle things Surveyors, finally, surveyed his land, among them George Washington. Surveys were able to set the western end of the river at what's now called The Fairfax Stone, but still, because of the vague terms of the original royal grant, the dispute between Lord Fairfax and the settlers Virginia had allowed onto his land land lasted for decades.
In the process of surveying, Washington was very taken with the region, and he and his family would settle in it. But he was also focused on the river. He would see the rocky character of the Potomac as a barrier to economic development of northern Virginia and had plans for making it navigable in 1770, almost immediately after the end of the Seven Years War.
The Atlantic colonies often made extravagant claims to the west. One of the more extravagant, Connecticut extended its northern and southern boundaries all the way to the Mississippi watershed, to Spanish territory. That meant its claim had to hop over New York's Hudson Valley and include about half of Pennsylvania: and of course Pennsylvania and New York were somewhat annoyed by this, to put it mildly. It would have also taken up what's now northern Ohio, southern Michigan, and southern Minnesota. Most all of these extravagant claims by the states were settled in the Northwest Ordinances of 1784, 1785 and 1787, in which the new territories were to be defined and eventually allowed into the Confederation as new states. As a part of that definition, the Northwest Ordnance of 1784 importantly also set out the method by which they were to be surveyed. The new Confederation did not want anymore land disputes.
I forgot to add ( noting your name, I should say, by Toutatis!) that the uncertain location of the headwaters of the Potomac not only would create a problem for defining the boundaries of the Northern Neck, but also created a small problem defining the south western boundary between West Virginia and Maryland that wasn't resolved until the Supreme Court settled it in Maryland vs West Virginia in 1910.
