Polarization is threatening the stability of democratic societies. Until now, polarization research has focused on opinion extremeness, overlooking the correlation between different policy issues. In this paper, we explain the emergence of hyperpolarization, i.e., the combination of extremeness and correlation between issues, by developing a new theory of opinion formation called “Weighted Balance Theory (WBT)”. WBT extends Heider’s cognitive balance theory to encompass multiple weighted attitudes. We validated WBT on empirical data from the 2016 National Election Survey. Furthermore, we developed an opinion dynamics model based on WBT, which, for the first time, is able to generate hyperpolarization and to explain the link between affective and opinion polarization. Finally, our theory encompasses other phenomena of opinion dynamics, including mono-polarization and backfire effects.