Matching methods are widely used to reduce confounding effects in observational studies, but conventional approaches often treat all covariates as equally important, which can result in poor performance when covariates differ in their relevance to the study. We propose the Priority-Aware one-to-one Matching Algorithm (PAMA), a novel semi-supervised framework that learns a covariate importance measure from a subset data of units that are paired by experts and uses it to match additional units. It optimizes a weighted quadratic score that reflects the relevance between each covariate and the study, and iteratively updates the covariate importance measure in the score function using unlabeled data. PAMA is model-free, but we have established that the covariate importance measure -- the learned weights -- is consistent when the oracle matching rule aligns with the design. In addition, we introduce extensions that address imbalanced data, accommodate temporal covariates, and improve robustness to mispaired observations. In simulations, PAMA outperforms standard methods, particularly in high-dimensional settings and under model misspecification. Applied to a real-world study of in-person schooling and COVID-19 transmission, PAMA recovers nearly twice as many expert-designated matches as competing methods using baseline covariates. A self-taught learning extension improves performance in simulations, though its benefit is context-dependent. To our knowledge, PAMA is the first framework to apply semi-supervised learning to observational matching with covariates of unequal relevance. It offers a scalable and interpretable tool for incorporating expert insight into policy-relevant observational research.