Accurate mass measurement is vital to modern industry and logistics. In closed pneumatic conveying of powdered materials, current solutions are bulky and expensive. And they rely on hardware to gain accuracy, which raises capital and maintenance costs. Therefore, adoption in warehousing, port handling, and blending lines remains limited. To address these limitations, we propose a streaming weighing method that maintains measurement accuracy while simplifying the mechanical design. We combine a perception algorithm with multimodal sensor fusion to reduce reliance on complex mechanisms and enable a lightweight, intelligent streaming metering system. We develop a Streaming Weighing Network (SWN) based on a process neural network (PNN) that fuses three sensor streams—weight, velocity, and vibration—for dynamic, high-precision mass estimation. Experiments on a prototype show a 99.67% reduction in system cost with only 0.5% loss in measurement accuracy. This provides a practical path to low-cost dynamic weighing equipment and a viable option for streaming metering of powdered materials.