With the growing ubiquity of wearable devices, sensed physiological responses provide new means to connect with others. While recent research demonstrates the expressive potential for biosignals, the value of sharing these personal data remains unclear. To understand their role in communication, we created Significant Otter, an Apple Watch/iPhone app that enables romantic partners to share and respond to each other's biosignals in the form of animated otter avatars. In a one-month study with 20 couples, participants used Significant Otter with biosignals sensing OFF and ON. We found that while sensing OFF enabled couples to keep in touch, sensing ON enabled easier and more authentic communication that fostered social connection. However, the addition of biosignals introduced concerns about autonomy and agency over the messages they sent. We discuss design implications and future directions for communication systems that recommend messages based on biosignals.