Predicting the evolution of mortality rates plays a central role for life insurance and pension funds. Various stochastic frameworks have been developed to model mortality patterns taking into account the main stylized facts driving these patterns. However, relying on the prediction of one specific model can be too restrictive and lead to some well documented drawbacks including model misspecification, parameter uncertainty and overfitting. To address these issues we first consider mortality modelling in a Bayesian Negative-Binomial framework to account for overdispersion and the uncertainty about the parameter estimates in a natural and coherent way. Model averaging techniques, which consists in combining the predictions of several models, are then considered as a response to model misspecifications. In this paper, we propose two methods based on leave-future-out validation which are compared to the standard Bayesian model averaging (BMA) based on marginal likelihood. Using out-of-sample errors is a well-known workaround for overfitting issues. We show that it also produces better forecasts. An intensive numerical study is carried out over a large range of simulation setups to compare the performances of the proposed methodologies. An illustration is then proposed on real-life mortality datasets which includes a sensitivity analysis to a Covid-type scenario. Overall, we found that both methods based on out-of-sample criterion outperform the standard BMA approach in terms of prediction performance and robustness.