This paper introduces a noise-tolerant computing method for over-the-air computation (AirComp) aimed at weighted averaging, which is critical in various Internet of Things (IoT) applications such as environmental monitoring. Traditional AirComp approaches, while efficient, suffer significantly in accuracy due to noise enhancement in the normalization by the sum of weights. Our proposed method allows nodes to adaptively truncate their weights based on the channel conditions, thereby enhancing noise tolerance. Applied to distributed Gaussian process regression (D-GPR), the method facilitates low-latency, low-complexity, and high-accuracy distributed regression across a range of signal-to-noise ratios (SNRs). We evaluate the performance of the proposed method in a radio map construction problem, which involves visualizing the radio environment based on limited sensing information and spatial interpolation. Numerical results show that our approach maintains computational accuracy in low-SNR scenarios and achieves performance close to ideal conditions in high SNR environments. In addition, a case study targeting a federated learning (FL) system demonstrates the potential of our proposed method in improving model aggregation accuracy, not only for D-GPR but also for FL systems.