Percentage study weights in meta-analysis reveal the contribution of each study toward the overall summary results and are especially important when some studies are considered outliers or at high risk of bias. In meta-analyses of test accuracy reviews, such as a bivariate meta-analysis of sensitivity and specificity, the percentage study weights are not currently derived. Rather, the focus is on representing the precision of study estimates on receiver operating characteristic plots by scaling the points relative to the study sample size or to their standard error. In this article, we recommend that researchers should also provide the percentage study weights directly, and we propose a method to derive them based on a decomposition of Fisher information matrix. This method also generalises to a bivariate meta-regression so that percentage study weights can also be derived for estimates of study-level modifiers of test accuracy. Application is made to two meta-analyses examining test accuracy: one of ear temperature for diagnosis of fever in children and the other of positron emission tomography for diagnosis of Alzheimer's disease. These highlight that the percentage study weights provide important information that is otherwise hidden if the presentation only focuses on precision based on sample size or standard errors. Software code is provided for Stata, and we suggest that our proposed percentage weights should be routinely added on forest and receiver operating characteristic plots for sensitivity and specificity, to provide transparency of the contribution of each study toward the results. This has implications for the PRISMA-diagnostic test accuracy guidelines that are currently being produced.