Below is an excerpt from The History of Merrimack and Belknap Counties, New Hampshire, published in Philadelphia by J.W. Lewis & Co. in 1885.
Weirs and Lake Winnipesaukee: The vicinity of Weirs, which lays just within the limits of Laconia and at the outlet of Lake Winnipesaukee, has been famous as a summer resort further back, probably, than the historical or traditionary records exist. Long before the white men invaded New England, the Winnipesaukees, a branch of the Penacook tribe of Indians, maintained a permanent "ahquedaukenash" or fish-weir at the outlet of the lake, and all the tribes in the vicinity would gather to participate in the spring and fall catch of shad. The weir was constructed by placing large boulders in an irregular line across the river at a proper distance from the outlet. The rocks were generally placed some ten feet apart, and a matting woven of twigs and tough bark was strung from rock to rock entirely across the stream, leaving a narrow opening in the center of the weir, through which the fish might pass to enter the waters of Lake Winnipesaukee. When the shad would reach the weirs and crowd through the opening was the red man's harvest-time. The braves would man the canoes, and, paddling out among the struggling fish, with spear and dig-net would soon fill the boat to the water's edge and return to the shore to deliver the shad to the squaws. The fish were split open and cleaned, and either laid out to dry on flakes or hung up and smoked for winter use. This wholesale method of fishing was also indulged in to a certain extent by the early settlers, and as shad were plenty in those days, many loads were used to enrich the soil on the high ground in the vicinity of the river. The weir was constsructed in a substantial manner and portions of it remained long after the mill-dams on the Merrimack had stopped the annual visitation of the shad; and now, although the Indian, the shad and the ahquedauken are among the things of the past in this vicinity, the name by which the locality is known still remains, and the Weirs is today one of the most popular summer resorts in New Hampshire.
Below is an article from the official program for Laconia's 1936 Aquedoctan Bicentennial Celebration.
According to Frederick Matthew Wiseman, an Ahquedaukenash is not a fish weir, but rather the "Eastern Abenaki name for the outlet to Lake Winnipesaukee", or Weirs Beach. The correct Abenaki name for a fish weir, states Wiseman, is not Ahquedaukenash, but "seniganial". Wiseman writes, "We made fish corrals, called seniganial, out of stone or sticks driven into the mud. Fish would swim into the corrals, become confused and be unable to swim out. Dipnets could then take the captive fish. One of our old corrals has been found in Wiwinebaski, near Ahquedaukeanash..."
Wiseman continues, "During this time [the Years of the Beaver, 1600-1820], the fish ran in our rivers to spawn, as they always had, and the traps, weirs, and spears we used in the past continued to be important. Indeed, Seniganitegw (Lewis Creek, Vermont) was called "stoneworks river" to commemorate the stone weirs that funneled the fish into our adelahiganak (basket traps), nets, and spears. When middle spring, the fishing moon, was upon us, we left our villages for namaskon (fishing camp) at Ahquedaukenash...and other places where the fish congregated. We remember families camping to repair and fill the fish drying racks...Fish were abundant, and many were prepared, cooked, and eaten on the spot until we could eat no more. When the fish were dry...they were placed in baskets, hide covers, or canoes to be taken back to the main village for permanent storage." (From p. 45 and p.86, The Voice of the Dawn: An Auto-History of the Abenaki Nation, 2001, University Press of New England, Hanover, NH.)
Other links of interest on this topic are:
The History of Manchester, New Hampshire, written by Chandler Eastman Potter in 1851. Chapter IV is titled "Manners and Customs of the Pennacooks, Ahquedaukenash or Weirs", and can be read in its entirety here (text copy) or here (image copy.)
The Merrimac River, Its Source and Its Tributaries, by J.W. Meader, 1869. Chapter IV is titled "The Forks - Winnipeaukee Lake and River", and details about the Ahquedaukenash can be read here.
More recently, The Indian Heritage of New Hampshire and Northern New England, by Thadeus M. Piotrowski, 2002, is a contemporary telling of the story; a preview on Google has a great map showing the tribal distribution of New Hampshire before white settlement.