The mixture of socio-economic classes, ethnicities, and cultures that characterizes many cosmopolitan urban areas can contribute to unequally perceived impacts of extreme weather events and, hence, need and responsibility for adaptation. Awareness of these differences is, as we argue, decisive for effective adaptation. This study explores the relationship between person-specific, socio-economic characteristics that are frequently associated with social vulnerability and the perception of current affectedness by extreme weather events, future impact severity as well as adaptation need and adaptation responsibility. Weuse a large online questionnaire survey from New York City studying two extreme weather events, heatwaves and heavy rainstorms. Wefind that previous harm is the most important factor across all tested models for both weather events. However, previous harm and affectedness do not well explain the perception of future impacts, whereas they correspond to views about adaptation responsibility; respondents who felt significantly more affected in the past perceive the community to be in charge of adaptation. Women (during both weather events) and the elderly (during heatwaves) state largest affectedness during past events, and see the community as being responsible for future adaptation. Hispanic and African American respondents, on the other hand, were identified to perceive adaptation to be more of an individual task-potentially related to previous experience with (a lack of) local government services in their areas. Our findings evoke equity questions, and can aid urban decision makers aiming to implement effective and just adaptation measures, targeting vulnerable socio-economic groups in New York City and potentially other cosmopolitan areas.