In this case, "Weimar Period" does not refer to a discrete political/cultural epoch in German history, but a way to periodize and individual's life. This is not an uncommon method in art history, which can break down an artist's life by aesthetic trends, such as Picasso's Blue Period, or residence, such as David Bowie's Berlin trilogy period. As the linked Bowie piece asserts, these cultural world of geographic locations often have a zeitgeist in which bleed into the art. Weimar in this period was influenced both by the Enlightenment and the growing cosmopolitanism of the music scene in Europe. The Weimar court orchestra started working with Italian styles and this was one of Bach's exposures to this form of music. The Weimar period also saw Bach's growing independence as a composer and moves away from being a purely court musician.

Scholars suspect that Nos. 1, 3, and 6 may have been written much earlier than the others, perhaps dating from Bach's Weimar period (1708-1717)

Seems to me it just refers to the time that Bach lived in Weimar (A city in Germany), not the Weimar period in German history in between the world wars.