Edge sensing can achieve high-performance state estimation in industrial IoT systems by supporting task offloading and data processing at powerful edge estimators. Accurate edge sensing depends on low offloading delay. However, it is challenging to decrease offloading delay due to the harsh industrial environment and limited communication-and-computation resources. In this article, a closed-form expressing of estimation error with respect to offloading delay is derived to indicate that adjusting offload delay on demand is necessary for estimation error reduction. Then, we propose an adaptive edge sensing scheme, aiming to minimize estimation error by jointly optimizing task offloading and sensor scheduling. The required optimization is formulated as a mixed-integer nonlinear programming problem and solved by the designed decomposition and approximation methods. Specifically, the maximum matching is used for sensor scheduling to assign the optimal edge estimator for each sensor. The task offloading algorithm is designed based on the inner approximation method to reduce the offloading delay. Finally, simulation results demonstrate that the proposed scheme has superiorities in reducing estimation error compared with centralized sensing and distributed sensing schemes. Moreover, we find an interesting result that estimation error is delay sensitive when the offloading delay is large.