The OED indicates that the relevant evolution of senses was

1. The quality of being equal or fair [1315]

3. The recourse to general principles of justice to correct or supplement the provisions of the law [1574]

4. In England (hence in Ireland and the United States), the distinctive name of a system of law existing side by side with the common and statute law. [1591]

5. a. An equitable right, i.e. one recognizable by a court of equity. [1629]

5. c. The ordinary shares of a limited company. They carry the right to the residue of a company's assets after it has paid all its creditors, and share in the distribution of profits. [1904]