Weizsäcker, who was born at Kiel in Germany, studied at the universities of Berlin, Göttingen, and Leipzig, obtaining his PhD from Leipzig in 1933. Between 1933 and 1945 he taught successively at the universities of Leipzig, Berlin, and Strasbourg. In 1946 he returned to Göttingen as director of physics at the Max Planck Institute where he remained until 1957, when he was appointed professor of philosophy at Hamburg. In 1970 he moved to Starnberg as director of the Max Planck Institute on the Preconditions of Human Life in the Modern World, a post he occupied until his retirement in 1980.

Weizsäcker proposed solutions to two fundamental problems of astrophysics. In 1938 he tackled the problem of how stars like the Sun can continue to radiate colossal amounts of energy for billions of years. Independently of Hans Bethe, he proposed a chain of nuclear-fusion reactions that could proceed at the high temperatures occurring in the dense central cores of stars. In this sequence, called the ‘carbon cycle’, one carbon nucleus and four hydrogen nuclei, or protons, undergo various transformations before ending the cycle as one carbon nucleus and one helium nucleus. The process involves the release of an immense amount of energy that is eventually radiated from the star's surface mainly as heat, light, and ultraviolet radiation. As the stars are rich in hydrogen, it was now clear that they could continue radiating until their core hydrogen was consumed.

In 1944 Weizsäcker proposed a variation of the nebular hypothesis of Pierre Simon de Laplace to account for the origin of the planets. Beginning with the Sun surrounded by a disk of rotating gas he argued that such a mass would experience turbulence and break up into a number of smaller vortices and eddies. Where the eddies met, conditions were supposed to be suitable for planets to form from the continuous aggregation of progressively larger bodies. The system did not, however, explain the crucial point of how the planets managed to acquire so much angular momentum, a property that is conserved and cannot just be created out of nothing. Modifications and additions later proposed by Hannes Alfvén and Fred Hoyle on this issue used forces generated by the Sun's magnetic field as the means of transmitting momentum and won a fair amount of support for the theory.