Accurate measurement of blade root loads is of critical engineering value for fatigue life assessment and health management of wind turbine blades. Current direct measurement methods suffer from high hardware cost, insufficient long-term operational reliability and difficulty in large-scale deployment. In contrast, the standard supervisory control and data acquisition (SCADA) system equipped on wind turbines provides a feasible low-cost alternative for indirect blade root load measurement. To address the insufficient measurement accuracy caused by strong coupling and non-stationary characteristics of multi-source SCADA sensing data, this paper proposes a SCADA-data-based virtual sensing method for blade root loads, which employs a symmetry-aware spatiotemporal deformable Transformer (SADeformer) for high-precision load inversion. In the feature extraction stage, the model adopts a collaborative architecture of variable-dimension deformable attention block (V-DAB) and time-dimension deformable attention block (T-DAB) to respectively capture nonlinear inter-variable dependencies and both long short-term temporal correlations, respectively. The model then outputs flapwise and edgewise load sensing results of three blades via a multi-layer perceptron predictor. Moreover, by integrating the prior physical knowledge of wind turbine blade symmetry, a new symmetry loss function is designed to model the spatial consistency of blade flapwise and edgewise loads. Experimental results demonstrate that the proposed method achieves state-of-the-art performance in second-level load data inversion, with a coefficient of determination (R2) of up to 0.952 and a mean absolute percentage error (MAPE) as low as 0.8%, outperforming mainstream time series models in comprehensive performance. The introduction of symmetry physical constraint significantly reduces three-blade load measurement errors, verifying the effectiveness of the proposed method.