Following the seminal paper by Altonji and Segal (1996), empirical studies have widely embraced equal or diagonal weighting in minimum distance estimation to mitigate the finite-sample bias caused by sampling errors in the weighting matrix. This paper introduces a new weighting scheme that combines cross-fitting and regularized weighting matrix estimation. We also provide a new cross-fitting standard error, applying cross-fitting to estimate the asymptotic variance. In a many-moment asymptotic framework, we demonstrate the effectiveness of cross-fitting in eliminating a first-order asymptotic bias due to weighting matrix sampling errors. Additionally, we demonstrate that some economic models in the earnings dynamics literature meet certain sparsity conditions, ensuring that the proposed regularized weighting matrix behaves similarly to the oracle weighting matrix for these applications. Extensive simulation studies based on the earnings dynamics literature validate the superiority of our approach over commonly employed alternative weighting schemes. (with by Xu Cheng, Alejandro Sanchez-Becerra)