Entering the 13th century, the Western Norse settlements consisted of:
Iceland
Greenland: Eastern & Western Settlements
Leifsbuðir, the outpost on the northern tip of modern Newfoundland
Straumfjorð, in the northeast of modern Nova Scotia
Humarvik, in the southwest of modern Nova Scotia
Skrælige
Most of the settlements were doing well, or at least sustaining themselves, but Leifsbuðir and Humarvik were not. Leifsbuðir was really only able to sustain a small ship repair outpost, and permanent settlement exhausted the natural resources nearby. By 1225, the last permanent residents left, and Leifsbuðir became an uninhabited stopover point on the journey westward.
By the 1250s, Humarvik was the next to go. A combination of conflict with the Mi'kmaq, bad harvests, and disease meant that the remaining inhabitants packed up and left. Some went to Straumfjorð further east, but a decent portion moved to Skrælige, growing its population further.
Further east, the Kingdom of Norway was reaching its peak. In 1261 Greenland formally joined Norway. Then from 1262 to 1264 the chieftains of Iceland and the Kingdom of Norway made an agreement known as the Old Covenant. These changes led to increased trade between Greenland, Iceland, and Norway, as well as an increase in settlement of Iceland. (Greenland was a bit too cold to convince most people to move there.)
This left Straumfjorð and Skrælige as the only remaining settlements outside of the kingdom of Norway. The abandonment of Leifsbuðir and Humarvik made the trans-Atlantic trade route more dangerous, and the new focus on Iceland and Greenland led to a further decline in trade. At this point, it just wasn't feasible to try and formally incorporate the areas into the crown, though the trade put them within Norway's sphere of influence regardless.
Back in Skrælige, growth led to an increase in demand for metal. Iron, bronze, and other metals had been supplied from the east, and some very limited mining of native copper supplemented this. In 1243 a small mining settlement was built to the southeast, by a cave on the side of Mount Þorr. Previous visits to the cave had reveled extensive native copper deposits, and so it was turned into a mine. The addition of a smelter allowed for bronzemaking, which was not commonly practiced anywhere else in North America at the time. In fact, metallurgy in general was uncommon in North America (source), apart from some limited use of native copper. While the new bronze wasn't as strong as iron or steel, it was now the strongest metal in North America.
On top of the new mining operation, winemaking grew into a substantial industry as well. Vinland, the name for the region around Leifsbuðir, was named for the vines of grapes that grew there. Skrælige's soil was even better suited for growing grapes, but hadn't had a substantial farm for growing them. Some emigrants from Leifsbuðir changed that, beginning large-scale winemaking operations in the countryside around Skrælingborg.
By 1300 the practice of slavery was extinct. There had only been 12 þrælls in 1200, and in the years that followed most of their kids were granted freedom. There were no new slaves added - with no wars there were no prisoners taken for slavery, and none imported - and this led to the practice's extinction. Part of this was cultural opposition - many people immigrated to Skrælige for their own freedom from their prior life, so they weren't really disposed towards taking slaves of their own.
After the manntal of 1200, some supplemental counts of the population had been made, but there hadn't been a thorough recounting yet. By 1300, the need to do so was clear, and once again a full count was done. The results were as follows:
Skrælingborg: 545 (+231)
Within the walls: 248 (+69)
Immediately east of the walls: 51
Immediately south of the walls: 15
Immediately west of the walls: 18
North & Docks: 147
Vinstrileið village: 20 (-)
Hœgrileið village: 29 (-5)
Scattered nearby: 17 (+3)
Miðrtunga: 109 (+48)
Norðstaðr: 15 (-2)
Eirsteinn: 20
Smarvik: 62 (+5)
Total population of 751.
The Abenaki village nearby also grew to roughly 100 inhabitants, recovering most of its prior losses due to disease.
With the abandonment of other settlements came an influx of people into Skrælige. While more housing was built in Skrælingborg, the need for a new village was clear. In 1350 a new settlement was built on the coast, Nyrvænn. While its coastal location would make it good for trade, the abandonment of settlements meant that European trade was on the decline. Instead, the village mainly relied on fishing and some farming for sustenance.
With all of the new immigration, relations with the native Abenaki grew strained. The larger population emboldened some new Skræligens to move further inland for fishing and hunting. Initially the Abenaki were somewhat forgiving, but further intrusions gave them no other choice. In the dead of night on the 15th of May, 1374, a band of Abenaki snuck into the edge of Miðrtunga and set fire to the village. By the time the sun came up on the 16th, half of the village was destroyed.
An emergency meeting of the Þing was called, and a group of men and women armed themselves to launch a counter attack on the nearby Abenaki village. It did not go well. As the Skræligens marched through the woods, they were ambushed by Abenaki arrows. Around 100 had entered the woods, and only 28 returned home. A handful were made captives, but the rest were killed in battle. Subsequently a peace offering was made - return of the captives, in exchange for several sheep, pigs, and a promise that the Skræligens never set foot further inland than Miðrtunga. The Þing agreed to the terms, and the fragile links between the Skræligen and Abenaki communities were completely severed.
Throughout the 14th century, the population of Skrælingborg continued to grow. Despite the lessening trade, it was enough to support a decent base of artisans within the city. Denser multi-storey half-timbered housing was built between the main walled settlement and the Floðveggr. This allowed for the population north of the original walls to more than double, and shifted the center of population northward.
After the May 1374 conflict, the need for better defenses was apparent. With the new housing being built, most of Skrælingborg's residents lived outside of the wall's protection. Over the next few years, a new stone wall was built that would replace the old wooden palisades and connect up to the Floðveggr.
In 1380 grim news arrived from the East - Straumfjorð was emptying out, and now the nearest inhabited Norse settlement would be Greenland. The settlements in Greenland weren't doing especially well either - the "Western Settlement" had been abandoned a couple of decades earlier (due to a combination of a colder climate, erosion, and conflict with incoming Thule people), and the "Eastern Settlement" was past its heyday. Straumfjorð was completely abandoned by the end of 1382, and this meant that the journey east was no longer feasible. Trade from the east was already on the decline, and this meant it came to an end. The conflict of 1374 meant that local trade was no longer an option either - Skrælige would have to be self-sufficient. This began a period known in Skræligen history as the "Isolation", where contact with the Old World was lost for over a century.
The Manntal of 1400 reported the following:
Skrælingborg: 893 (+348)
Church & Market District (Inside the old walls): 248 (-)
Miðrway & Docks (Formerly North & Docks): 517 (+370)
Immediately east of the walls: 41 (-10)
Immediately south of the walls: 15 (-)
Immediately west of the walls: 18 (-)
Vinstrileið village: 20 (-)
Hœgrileið village: 17 (-12)
Scattered nearby: 17 (+3)
Nyrvænn: 233
Main Village: 182
North Village: 23
South Village: 28
Miðrtunga: 56 (-53)
Norðstaðr: 16 (+1)
Eirsteinn: 20 (-)
Smarvik: 58 (-4)
Total population of 1276.
The Manntal is a bit like the Domesday Book in England, except in Skrælige it was to be fully updated every century. For some reason in my head I thought that there was a second Domesday book that updated it. I think it was a misunderstanding though, while there was a "Little Domesday" and a "Great Domesday", they did not overlap with each other, and combined formed what we know of as the Domesday book.