Due to the unavoidable battery replacement or replenishment, diverse energy harvesting techniques have been integrated with Wireless Sensor Networks (WSNs) to overcome limited battery power and extend the network lifetime. However, variable transmission power levels based on non-uniform energy harvesting rates can incur asymmetric links. In this paper, we propose light-weight forwarding protocols to reliably deliver sensory data to a sink over time-varying asymmetric links in energy harvesting WSNs. A Weighted Confirmation (WCFM) scheme is proposed to differentiate multiple paths between a data source and a sink by assigning multiplicative weights on the paths. A Lazy Confirmation (LCFM) scheme is also proposed to assure a reverse path by waiting for extended communication range. In addition, an Asymmetric Link Aware Back off mechanism is proposed to avoid possible packet contentions and collisions. We evaluate the proposed techniques through extensive simulation experiments and their results indicate that the proposed forwarding protocols can be a viable approach in energy harvesting WSNs.