The mean relatedness of an individual to others in its social group may change with age. Such kinship dynamics, which are expected to influence sex- and age-specific social behaviours, are sensitive to demography. Existing models of kinship dynamics, however, have focused chiefly on the influences of population-level demographic parameters (e.g., sex-specific dispersal rate and mating pattern). Here, we extend these models to explore the effects of local group size on kinship dynamics and the resulting patterns of selection for sex- and age-specific helping and harming. We show that individuals’ average relatedness to others is higher in smaller than larger groups, and consequently, selective pressure for helping or harming is generally stronger in smaller than larger groups. Moreover, relatedness changes faster with age in smaller groups, particularly at younger ages. These patterns favour more extreme social traits in smaller groups and especially so at earlier life history stages. In particular we highlight that, while social systems characterized by bi-sexual philopatry with non-local mating (e.g., whales) are known to favour a shift from more helpful to more harmful behaviour as females age — a trend that has been invoked to explain the evolution of menopause and post-reproductive helping — the timing of this shift is predicted to be sensitive to local group size, potentially favouring earlier female reproductive cessation in smaller groups. Our study generates new insights into the effects of local group properties on kinship dynamics, and suggests that such effects might also help to explain widespread variation in age-linked social traits, such as the timing of menopause in social mammals.