Using single-pixel detection, the end-to-end neural network that jointly optimizes both encoding and decoding enables high-precision imaging and high-level semantic sensing. However, for varied sampling rates, the large-scale network requires retraining that is laboursome and computation-consuming. In this letter, we report a weighted optimization technique for dynamic rate-adaptive single-pixel imaging and sensing, which only needs to train the network for one time that is available for any sampling rates. Specifically, we introduce a novel weighting scheme in the encoding process to characterize different patterns' modulation efficiency. While the network is training at a high sampling rate, the modulation patterns and corresponding weights are updated iteratively, which produces optimal ranked encoding series when converged. In the experimental implementation, the optimal pattern series with the highest weights are employed for light modulation, thus achieving highly-efficient imaging and sensing. The reported strategy saves the additional training of another low-rate network required by the existing dynamic single-pixel networks, which further doubles training efficiency. Experiments on the MNIST dataset validated that once the network is trained with a sampling rate of 1, the average imaging PSNR reaches 23.50 dB at 0.1 sampling rate, and the image-free classification accuracy reaches up to 95.00\% at a sampling rate of 0.03 and 97.91\% at a sampling rate of 0.1.
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