We present a novel instance-based approach to handle regression tasks in the context of supervised domain adaptation under an assumption of covariate shift. The approach developed in this paper is based on the assumption that the task on the target domain can be efficiently learned by adequately reweighting the source instances during training phase. We introduce a novel formulation of the optimization objective for domain adaptation which relies on a discrepancy distance characterizing the difference between domains according to a specific task and a class of hypotheses. To solve this problem, we develop an adversarial network algorithm which learns both the source weighting scheme and the task in one feed-forward gradient descent. We provide numerical evidence of the relevance of the method on public data sets for regression domain adaptation through reproducible experiments.