A critical performance criterion in backscatter modulation-based RFID sensor networks is the distance at which a RFID reader can reliably communicate with passive RFID sensors (or tags). This paper proposes to introduce a power amplifier (PA) and an energy storage device (such as a capacitor or a battery), in the hardware architecture of conventional passive RFID tags, with the aim of allowing amplification of the backscatter signal to increase the read range. This new tag architecture, referred to as Amplified Backscattering via Energy Harvesting (ABEH), can still be considered as passive, since the energy storage device is charged exclusively by harvesting energy from the RF-signal transmitted by the reader and received by the tag during idle periods. The harvested and stored energy is then used by the tags to opportunistically amplify the backscatter signal. It is noted that this architecture is significantly different from active RFID tags where the battery, charged at the time of installation, is used to supply a complete onboard transceiver so that no backscatter modulation is employed. Energy scheduling strategies, based on the trade-off between energy harvesting rate and successful transmission probability, are proposed. Performance analysis of tags with the proposed ABEH architecture is carried out over quasi-static fading channels by framing the design problem as a Markov Decision Process. Numerical results show remarkable improvement of the ABEH approach with respect to conventional passive RFID tags and provide insight into the effect of system parameters on the energy scheduling.