It was the Berlin republic (and nominally, an empire still, the Deutsches Reich, thus the Reichstag) as the government moved to Weimar (not "Wiemar") only during a short lived period of the Communist uprising that lasted 1 week. After the badly-organized revolutionary "Spartacists" in the city were ruthlessly put down in short order (and their incompetent, relucant and actually pacifistic leaders tortured and murdered by soldiers, with the Bolshevik advisor/manipulator/mastermind sent by Lenin escaping unlike them), the government moved back to Berlin, where it stayed.

Germany is a (Bundes)republik only nowadays. And used to be a "Bonn republic" due to the Communist occupation of East Berlin, again, but for a long time. But back then it was still the Berlin... empire, actually. And there was never a "third" Reich as it was always the second, the first being the so-called Holy Roman Empire of the German Nation.