Obergefell v. Hodges is an extended essay on tradition, but the majority and the dissent have very different ways of articulating what constitutionally protected tradition is and how we recognize its contours.
Justice Kennedy argues that constitutionally protected traditions are those which are consistent with the reasons why a social tradition is valuable to us today. "[I]n assessing whether the force and rationale of its cases apply to same-sex couples, the Court must respect the basic reasons why the right to marry has been long protected." Therefore he recites four features of marriage that make it valuable to us today and then argues that same-sex marriage applies to all of them. His opinion assumes that tradition--or at the very least, constitutionally protected tradition--is something that present generations can reason about and rationally extend or alter. Kennedy's recitation of how the couples in the case met, fell in love, married, lived, and raised children in Obergefell is not just an attempt to tug at our heartstrings. He is also trying to show that the reason we sympathize with these couples and their plight is the same reason we sympathize with the hardships and sacrifices of married couples generally.
Roberts, Scalia, and especially Alito, identify constitutionally protected traditions with long-standing traditional practices. They view tradition as the accumulated wisdom of previous generations. Therefore we should not disturb the judgments of previous generations because we are very likely to make a mistake. We view matters from a very narrow perspective--our own lifetimes--and therefore if we try to make significant changes based on contemporary judgments and reasons we are likely to produce unintended and undesirable consequences, as well as destroying institutions of long-standing.
These different conceptions of tradition lead to different views about human knowledge and moral growth. Kennedy regards the evolution of tradition as beneficially shaped by increases in knowledge and understanding. Repeatedly he speaks of "new awareness," "new insight," or "enhanced understanding" of new facts and moral truths, that result from deliberation and political interaction. These recent insights and understandings should properly be incorporated into the constitutional tradition, altering what the tradition means for us today.
The dissenters, by contrast, do not think that present generations are necessarily getting any wiser, even if their values may have changed. At one point in his dissent, Chief Justice Roberts, almost in exasperation, exclaims, "Just who do we think we are?"
Kennedy emphasizes that traditional practices change over time and are always changing. Hence he offers a history of changing conceptions of marriage-- from arranged marriages to marriage for love to the gradual decline of coverture rules to the emergence of companionate marriage between equals. Roberts and Alito, by contrast, emphasize that core features of the institution of marriage have not changed for centuries, and can be found in almost all civilizations, ancient and modern. (Note Chief Justice Roberts' reference to "the Kalahari Bushmen and the Han Chinese, the Carthaginians and the Aztecs.") The changes that Kennedy describes are not central to the core of the tradition, while the union of one man and one woman is central.
It is tempting to identify the dissenters with Burke, and view Kennedy as opposed to Burkeanism. Certainly the dissenters would like to brand Kennedy as a revolutionary or Jacobin, heedlessly destroying a valued institution at the center of society. But this is a caricature of what Kennedy is actually doing in his opinion. Kennedy's use of tradition is also Burkean in its own way. He simply emphasizes different features of Burke's thought. In particular Kennedy emphasizes change through respect for tradition that results from discussion and lived experience--as opposed to change that occurs through violence and revolutionary upheaval. Kennedy emphasizes the natural evolution and growth of previous commitments through debate, contestation and social practice. Our commitments evolve as they we apply them to changed factual circumstances and our wisdom grows through encountering those changed circumstances in practical terms. We can have greater confidence in our judgments achieved in this way because, unlike previous generations, we have the benefit of their experience, while they do not have the benefit of ours.