It was based on a right to marry and equal protection, but did make a reference to a right to privacy as well:

> "The Constitution promises liberty to all within its reach," the Court declared, "a liberty that includes certain specific rights that allow persons, within a lawful realm, to define and express their identity." Citing Griswold v. Connecticut, the Court affirmed that the fundamental rights found in the Fourteenth Amendment's Due Process Clause "extend to certain personal choices central to individual dignity and autonomy, including intimate choices that define personal identity and beliefs,"

https://en.wikipedia.org/wiki/Obergefell_v._Hodges?wprov=sft...