Estimates of individual treatment effects from networked observational data are attracting increasing attention these days. One major challenge in network scenarios is the violation of the stable unit treatment value assumption (SUTVA), which assumes that the treatment assignment of a unit does not influence others' outcomes. In network data, due to interference, the outcome of a unit is influenced not only by its treatment (i.e., direct effects) but also by others' treatments (i.e., spillover effects). Furthermore, the influences from other units are always heterogeneous (e.g., friends with similar interests affect a person differently than friends with different interests). In this paper, we focus on the problem of estimating individual treatment effects (both direct and spillover effects) under heterogeneous interference. To address this issue, we propose a novel Dual Weighting Regression (DWR) algorithm by simultaneously learning attention weights that capture the heterogeneous interference and sample weights to eliminate the complex confounding bias in networks. We formulate the entire learning process as a bi-level optimization problem. In theory, we present generalization error bounds for individual treatment effect estimation. Extensive experiments on four benchmark datasets demonstrate that the proposed DWR algorithm outperforms state-of-the-art methods for estimating individual treatment effects under heterogeneous interference.