A novel distributed estimation method for sensor networks is proposed. The goal is to track a time-varying signal that is jointly measured by a network of sensor nodes despite the presence of noise: each node computes its local estimate as a weighted sum of its own and its neighbors' measurements and estimates and updates its weights to minimize both the variance and the mean of the estimation error by means of a suitable Pareto optimization problem. The estimator does not rely on a central coordination: both parameter optimization and estimation are distributed across the nodes. The performance of the distributed estimator is investigated in terms of estimation bias and estimation error. Moreover, an upper bound of the bias is provided. The effectiveness of the proposed estimator is illustrated via computer simulations and the performances are compared with other distributed schemes previously proposed in the literature. The results show that the estimation quality is comparable to that of one of the best existing distributed estimation algorithms, guaranteeing lower computational cost and time.