Practical technologies for the Internet of Things (IoT) must provide connectivity to all objects under a common framework irrespective of their size or value. Power requirement, cost of wireless devices and scalability have proved critical bottlenecks for the universal deployment of the IoT. One approach to address these issues is the use of a communication paradigm where the devices communicate via backscattering and exploit harvested power from an external RF source. In a Backscattering Tag-to-Tag Network (BTTN), the tags themselves are able to read and interpret the backscattered communications from other neighboring tags. In the tag-to-tag link, the BTTN tag has to demodulate a receiving signal with a low modulation index. In order to improve the link range, we propose a power-efficient demodulator design that enables the receiving tag to quantify the amplitude-shift keying (ASK) modulated signal with a modulation index as low as 0.6%. The demodulator consumes 1.21 µW at 1.1 V supply voltage at a data rate of 10 kbps.