This paper considers how webs of connection bridge people from different social worlds and engender affinity ties that can be mobilised to nurture caring relationships, despite the physical and cognitive borders that exist within and between societies. Territorial contestation between the Myanmar military and the Kachin Independence Army has precipitated internal displacement in Kachin state (Myanmar). The situation of Kachin internally displaced people in camps at the China–Myanmar border directs attention to how geographical and geopolitical constraints deter international humanitarian assistance yet provide opportunities to engage a different set of humanitarian actors. The paper first argues that Kachin internally displaced people are treated as surplus populations by the sovereign states in both Myanmar and China. Surplus populations come into existence when nation‐states impose punitive measures that compromise the survivability of populations that are considered threatening to national sovereignty. Second, the paper examines how mobilising affinity ties enables Kachin humanitarian workers to leverage the citizenship resources of empathetic Chinese nationals to negotiate humanitarianism constraints at the China–Myanmar border. Affinity ties refer to connections emanating from a dynamic constellation of cultural attributes to do with history, ethnicity, religion and place among other malleable identity constructs. Interlocking constellations form webs of connections that transverse essentialising categories of social difference and contribute to shared biographies that allow for cultivating emotional attachments to a place and its people. Affinity ties may congeal into durable ties of solidarity and activism, but no less significant are vernacular expressions of affinity that prompt empathy for proximate or distant strangers and a predilection to act on behalf of those experiencing oppression. The paper proposes that conceptualising affinity ties draws out transversal webs of connections that bridge people of differential social positionings. This approach provides a potential ethical stance and productive analytical lens for advancing wider migration and citizenship debates.