This study, the second volume of the series "Sources" of the "Max Planck Research Library for the History and Development of Knowledge," reviews a historical discussion about the question of whether a balance in equilibrium, after having been deflected, returns to its original position. This question captured the attention of philosophers and scientists for almost two millennia, from Greek antiquity to the sixteenth century when the "equilibrium controversy" became a central question among scholars. Two new sources related to this controversy are presented: an annotated copy of Jordanus de Nemore's "Liber de ponderibus" edited by Petrus Apianus in 1533 and an annotated copy of Giovanni Battista Benedetti's "Diversarum speculationum mathematicarum et physicarum liber" from 1585. Both works contain handwritten marginal notes by Guidobaldo del Monte, author of the most influential early modern text on mechanics. A detailed analysis of these sources, their prehistory, and their contexts shows that the "equilibrium controversy" only scratched the surface of a much deeper conceptual crisis of early modern mechanics that was triggered by the introduction of the medieval concept of "positional heaviness" into early modern discussions. This crisis helped to establish fundamental insights on which Galileo eventually built his theory of mechanics as well as his theory of motion.