Short answers, pulled from the story.
Weimar Classicism began in 1771, when the widowed Duchess Anna Amalia invited the Seyler Theatre Company to her court in Weimar. The movement later centered on Goethe and Schiller during the period from 1786 to 1805.
The movement's leading figures were Johann Wolfgang von Goethe and Friedrich Schiller, joined earlier by Christoph Martin Wieland and Johann Gottfried Herder. All four were drawn to Weimar in the Duchy of Saxe-Weimar.
It is named after the city of Weimar in the Duchy of Saxe-Weimar because its leading authors lived there. The movement combined ideas from Romanticism, Classicism, and the Age of Enlightenment into a new humanism.
Weimar Classicism drew on the German Enlightenment philosophy of Christian Thomasius and Christian Wolff, Immanuel Kant's critical philosophy, and Alexander Baumgarten's writing on aesthetics. Goethe and Schiller also relied on three of their own terms, Gehalt, Gestalt, and Stoff, to describe how art works.
Schiller's periodical Die Horen published a serialized novel, Agnes von Lilien, by his sister-in-law Caroline von Wolzogen. It also published Sophie Mereau, Friederike Brun, Amalie von Imhoff, Elisa von der Recke, and Louise Brachmann.
Between 1786 and Schiller's death in 1805, he and Goethe built a network of writers, philosophers, scholars, and scientists, including Alexander von Humboldt. This alliance became part of the foundation of nineteenth-century Germany's understanding of itself as a culture and of its political unification.