The fish weight, which indicates the growth rate of fish, is a crucial factor that optimizes the feeding rate and shapes the life history of fish in recirculating aquaculture systems. Estimating or predicting fish weight is essential for achieving better control of the output of an aquaculture system. However, many difficulties arise from the lack of direct measurement of fish weight. Currently, aquaculture sensors that directly estimate the fish's weight are unavailable. Additionally, the fish growth model that relies on the fish weight is affected by various environmental factors like water temperature, dissolved oxygen, salinity, and light, increasing the difficulty in estimating the weight. This paper proposes an extended Kalman filter approach for assessing the fish weight from directly available measurements of the fish stocking density and dissolved oxygen. The extended Kalman approach relies on a new version of the fish population growth model, which includes the fish population and dissolved oxygen dynamics. The simulation results demonstrate that the extended Kalman filter algorithm achieves good weight estimation in the nominal case and the presence of process and measurement noises.