Although still prevalent in many human societies, the practice of cousin marriage has precipitously declined in populations undergoing rapid demographic and socioeconomic change. However, it is still unclear whether changes in the structure of the marriage pool or changes in the fitness-relevant consequences of cousin marriage more strongly influence the frequency of cousin marriage. Here, we use genealogical data collected by the Tsimane Health and Life History Project to show that there is a small but measurable decline in the frequency of first cross-cousin marriage since the mid-twentieth century. Such changes are linked to concomitant changes in the pool of potential spouses in recent decades. We find only very modest differences in fitness-relevant demographic measures between first cousin and non-cousin marriages. These differences have been diminishing as the Tsimane have become more market integrated. The factors that influence preferences for cousin marriage appear to be less prevalent now than in the past, but cultural inertia might slow the pace of change in marriage norms. Overall, our findings suggest that cultural changes in marriage practices reflect underlying societal changes that shape the pool of potential spouses.