Registration of brain scans with pathologies is difficult, yet important research area. The importance of this task motivated researchers to organize the BraTS-Reg challenge, jointly with IEEE ISBI 2022 and MICCAI 2022 conferences. The organizers introduced the task of aligning pre-operative to follow-up magnetic resonance images of glioma. The main difficulties are connected with the missing data leading to large, nonrigid, and noninvertible deformations. In this work, we describe our contributions to both the editions of the BraTS-Reg challenge. The proposed method is based on combined deep learning and instance optimization approaches. First, the instance optimization enriches the state-of-the-art LapIRN method to improve the generalizability and fine-details preservation. Second, an additional objective function weighting is introduced, based on the inverse consistency. The proposed method is fully unsupervised and exhibits high registration quality and robustness. The quantitative results on the external validation set are: (i) IEEE ISBI 2022 edition: 1.85, and 0.86, (ii) MICCAI 2022 edition: 1.71, and 0.86, in terms of the mean of median absolute error and robustness respectively. Future work could transfer the inverse consistency-based weighting directly into the deep network training.