Energy Harvesting-Wireless Sensor Networks (EH-WSNs) play a crucial role in the development of Green Internet of Things (GIoT). While the energy-harvesting process alleviates the constraints of energy supply in WSNs, most current routing protocols for EH-WSNs inadequately account for the heterogeneity in energy states and traffic loads among sensor nodes, which may impair the energy efficiency and transmission performance of networks. To address the above issues, we utilize molecular diffusion theory to design an energy-balanced and load-aware routing algorithm (EBLARA-MD for short) for EH-WSNs. Initially, we construct a dual EH prediction model based on the clustering Markov chain (MC) method, to accurately forecast the amount of solar and wind power generation. Subsequently, an energy-rank model is established to assess the energy levels of nodes. Building on this, we propose a cross-layer adjustment scheme to avoid energy depletion and wastage. Namely, at the Media Access Control (MAC) layer, the backoff time is optimized dynamically to affect the channel access probability of each node; at the physical layer, the transmission power is determined adaptively by considering the wireless fading property. In addition, we construct a load-aware model to reflect the congestion degree of data buffer. Finally, we leverage molecular diffusion theory to allocate the routing probabilities for suitable paths. Simulation results demonstrate that the proposed routing algorithm achieves superior performance in terms of energy efficiency, end-to-end delay variance, and packet delivery ratio.