Specialist in Greek art and historiography; particularly known for his work on the Greek geometric pottery style. Schweitzer's father was Major Carl Georg Heinrich Schweitzer, a career soldier (Major) in the German infantry "Vogel von Falckenstein" division. His mother was Christiana Auguste Adeline Caroline Aneshänsel (Schweitzer). Schweitzer received his abitur from the Gymansium in Kalrsruhe in 1911. He studied at the universities in Berlin, under Georg Loeschcke and Heidelberg, receiving his doctorate from the latter under Friedrich von Duhn in 1917. His Heidelberg studies were augmented with courses from classicists Franz Boll (1867-1924), and the von Duhn student and ceramics scholar Rudolf Pagenstecher. His dissertation was on the topic of chronology of style in the Geometric period of Greek pottery. During these years he befriended Erwin Panofsky and the two remained lifelong friends. In the first World War Schweitzer was a flying instructor and test pilot; throughout his life he had a reputation of fearlessness (Fuchs). After completing his Habilitation in 1921 at Heidelberg with a topic on the concept of art and the artist in ancient art, he received a stipend to study at the Deutsches Archäologisches Institut (DAI or German Archaeological Institute) in Greece, but the hyper-inflation of the German mark meant that Schwetizer had to support himself as a musician (he was an accomplished piano player and adaquate violinist) and lecturer. He was apppointed Ordinarius professor at the University of Königsberg in 1925. He married Elisbeth Rudolph (b. 1907) in 1931. The following year he accepted a position at the University of Leipzig, replacing Franz Studniczka. During the war his note cards of all his research were destroyed and Schweitzer had to begin his research again, a loss he likened to a colleague's loss of wife and children.Following World War II Schweitzer was appointed the first Rektor of Leipzig University (1945/46) when philosopher Hans Georg Gadamer (1900-2002) was found unfit. He published a study on Roman Republic portraiture, Die Bildniskunst der römischen Republik in 1948. The same year he moved to Tübingen University, replacing Carl Watzinger. Beginning in the 1950s, Schweitzer returned to the study of Geometric-era Greek art, working on a magnum opus on the art of the period. He retired emeritus from the University in 1960. At his death in 1966, his work remained unpublished. It appeared in 1969 as Die geometrische Kunst Griechenlands and in an excellent English translation as Greek Geometric Art in 1971.
Schweitzer was a leading exponent of the Strukturforschung (structural research) school, a German theoretical notion attempting to replace the concept of style with a spatial structural analysis, which was linked to cultural identity. This group included Gerhard Krahmer, Gido Kaschnitz von Weinberg, and Friedrich Matz (1890-1974).