Dividing variables into groups is an intuitive idea for tackling large-scale multi-objective problems. However, regular grouping methods often suffer from the computationally expensive budget, resulting in the inflexibility of the division of variables. To remedy this issue, this paper proposes a Pearson correlation-based adaptive variable grouping method, which not only consumes no additional computational budget, but also is able to adaptively divide variables with the evolvement of solutions. According to our observation, variables with similar effects on objectives exhibit similar evolutionary trends. Therefore, the Pearson correlation coefficient is used to measure the similarities of the evolutionary trends of variables. Based on the Pearson correlation-based adaptive variable grouping method, this paper further designs a weighted optimization framework based on Pearson correlation-based adaptive variable grouping. Experiments and analyses are conducted on three popular test suites with up to 5000 decision variables. Extensive comparisons demonstrate that the proposed Pearson correlation-based adaptive variable grouping method is superior to existing grouping methods and the weighted optimization framework based on Pearson correlation-based adaptive variable grouping outperforms state-of-the-art optimizers.