Wireless powered sensor networks (WPSNs) have evolved as a promising paradigm for energy-efficient communications. Recently, the proliferation of reconfigurable intelligent surface (RIS) has further been envisioned as a cost-effective solution for improving wireless power transfer (WPT) efficiency. In this paper, from the practical perspective of balancing the network sustainability and reliability, we consider a RIS-enhanced partially WPSN that composed of wireless-powered energy receivers (ERs) and battery-powered information receivers (IRs). Assuming the partially WPSN operates in time division multiple access (TDMA) mode, the joint optimization of covariance matrices, downlink/uplink (DL/UL) time allocation and RIS reflecting coefficients are investigated under the minimum DL rate constraint among all IRs for maximizing the achievable UL sum rate. Specifically, the single-IR single-ER (SISE) case is first studied based on the assumption of separate DL/UL RIS reflecting coefficients, in which an alternating optimization algorithm is proposed with semi-closed-form optimal solutions. In order to reduce the hardware overhead and signal processing complexity, we also investigate the case of identical DL/UL RIS reflecting coefficients, in which an iterative optimization algorithm is developed to tackle the coupled DL/UL transmissions. Then, we extend our work to the multiple-IRs multiple-ERs (MIME) case, where both the optimization problems corresponding to separate and identical DL/UL RIS reflecting schemes become more challenging to solve. To circumvent this intractability, we propose a successive convex relaxation (SCA) based alternating optimization algorithm and a low-complexity two-step algorithm. Finally, numerical results demonstrate the superior UL sum rate performance of our proposed algorithms over the adopted benchmarks.