Satellite observations play a central role in monitoring atmospheric methane (CH₄), a potent greenhouse gas. Recently launched instruments such as TROPOMI provide unprecedented spatial coverage, however, heterogeneous sampling with both dense and sparsely covered regions poses challenges for inverse modeling systems. This uneven sampling can cause very densely observed areas to dominate the inversion and lead to vanishing gradients in sparsely covered regions.</p> <p>We present a parametric regularization method that computes observation-specific weighting factors based on the spatial and temporal distribution of measurements. Our method modifies the observational covariance matrix through a preprocessing step, homogenizing the effective weight of densely and sparsely sampled regions without introducing additional computational cost during the optimization. Since the parametric weighting is determined prior to the inversion, the approach can be used to calculate weights for multiple-instrument inversions, without further additional parameter tuning. The adaptive regularization is applied to global methane emission inversions for 2019, at 1&deg; &times; 1&deg; resolution, using the TMVar (TM5-MP/4DVAR v1.2.6 LAMOS) system, assimilating TROPOMI column observations.</p> <p>Compared to a constant regularization approach, the presented method reduces the relative variation in grid-cell weights by about 20 %, by strengthening constraints in high-latitude and oceanic regions. Posterior simulations from inversions that either assimilate satellite data only or also assimilate NOAA surface measurements are evaluated against independent TCCON column observations, showing that the method preserves overall inversion performance while improving the spatial balance of satellite influence. The resulting global methane budget is consistent with recent top-down estimates from the Global Methane Budget.