When people disclose information on social media that is sensitive or potentially stigmatized (e.g., mental illness, pregnancy loss), how do others decide to respond? We use interviews and vignettes to provide a response decision-making framework (RDM) that explains factors informing whether and how individuals respond to sensitive disclosures from their social media connections. The RDM framework includes factors related to the self, poster, and disclosure context (i.e., relational, temporal, social). Our findings include how people's decisions are complicated by balancing their own needs (e.g., privacy, wellbeing) as well as the posters’ (e.g., support) when seeing what they consider sensitive posts on social media. We identify empirically grounded insights and information that social media designs could surface to support both potential disclosers and responders. We argue that social media sites should provide privacy controls for both disclosers and responders, and facilitate the visibility of network-level support.