In the video, I thought the reason why the word “free” was in the name was because it was a Carnegie Library. I conducted some research and discovered that was not the case.
In the late 19th and early 20th centuries, there were subscription libraries. People paid to be members and had exclusive use of that particular library. A free library was open to the public.
The Cotton Free Library building no longer houses a library. It is sometimes rented out, though.
“The Cotton Free Library is the public library serving the town of Weybridge, Vermont. It is located on Quaker Village Road, in a small architecturally distinguished Colonial Revival building constructed in 1913 donated by Joshua Franklin Cotton. The building was listed on the National Register of Historic Places in 1996.
The Cotton Free Library is located in Weybridge’s historic village center, just north of Weybridge Town Hall, with which it shares a lot. It is a small square structure, built out of rock-faced concrete blocks and covered by a hip roof. Its front facade is symmetrical with the centered entrance sheltered by a gabled portico supported by two Doric columns. The centered of the gable is adorned with a small oculus window. The interior’s original features include a pressed tin ceiling, a swinging metal arm for holding an oil lamp, and a brass-plated tin chandelier with eight etched-glass globes, originally lit with kerosene but later electrified. The rear wall has a fireplace whose mantel is adorned with Arts and Crafts tiles. 
The library was founded in 1897 by the town after receiving a bequest from Joshua Franklin Cotton, a local citizen. Originally located in the basement of the town hall, its growing collection prompted the decision to build a dedicated structure. Land for the building was acquired in 1913, and construction took place in 1914-16, with the building formally opened late in 1916. The library is one of the only buildings of its type in the state to be built using this type of concrete block. The building was electrified in 1922.”-https://en.m.wikipedia.org/wiki/Cotton_Free_Library