We conducted a co-design study with 26 users in dyadic groups who were assigned to the opposing roles of "Streamers'' and "Viewers'' to design interactive, wearable telepresence prototypes for interpersonal use. The goal was to elicit values, identify value tensions, and resolve these tensions in the design of a system that allows Streamers to share their live experiences with a remote Viewer. Leveraging the lens of value-sensitive design (VSD), we found that these different stakeholders prioritized different values in design, but possibly due to our prompt to design for someone they cared about/knew, often accounted for one another's needs in their solutions to arrive at designs that were affordable, unobtrusive, and socially acceptable for the Streamer, while giving the Viewer a sense of autonomy. Our work highlights the strengths of co-design when eliciting important human values in the design of sociotechnical systems for wearable telepresence, reconciling value tensions, and conceptualizing novel hardware- and software-based solutions for enhancing the interpersonal telepresence experience of both viewers and streamers. A key insight from our study is that no single system will meet all users' needs; therefore, we should move towards building customizable toolkits to account for differing values and needs.