Here is what the Winnipesaukee Historical Society has about the Weirs. Shad, not salmon.
The native Abenaquis, members of the Penacook tribe, called their village Aquedoctan, meaning "place of good fishing". For fishing, they built a special type of basket, called a WEIR, to capture the abundant fish (shad) that migrated through the Weirs Channel on their way from Lake Winnipesaukee to the Merrimac river to the sea. Several WEIRS went into the channel to block the shad from passing through, effectively trapping them.
http://www.lwhs.us/wei-weirsbeach.htm