Domain adaptation (DA) approaches have received significant attention in industrial cross-domain fault diagnosis. However, the scarcity of sufficient labeled fault data, particularly under varying loading conditions and harsh operational environments, can give rise to distinct label spaces between two domains, thereby impeding the application of DA-based diagnosis methods. In this paper, we propose a novel dual-weight domain adversarial network (DWDAN) for diagnosing partial domain faults of feedwater heater system in a large-scale power unit, where the target label space is a subset of the source domain. Firstly, domain adversarial network with an instance-based feature learning strategy is constructed to capture domain-invariant and class-discriminative features hidden in raw process data, thereby enhancing feature extraction and generalization abilities of fault diagnosis. Furthermore, a dual-stage reweighted induction module is designed to quantify the contribution of samples from both class-level and sample-level for selective adaptation. This module can automatically eliminate outlier fault categories in the source domain and facilitates alignment of feature distributions for shared fault categories. Comprehensive experiments conducted on the feedwater heater system of a 600 MW coal-fired generating unit demonstrate the outstanding performance of DWDAN.