At present, most recommender systems involve two stakeholders, providers and customers. Apart from maximizing the recommendation accuracy, the fairness issue for both sides should also be considered. However, there is a trade-off for multi-objective optimization problems, where optimizing one objective (e.g. provider-side fairness) may degrade the performance of others (e.g. accuracy). Most of previous studies try to improve two-sided fairness with post-processing algorithms or fairness-aware loss constraints, which are highly dependent on the heuristic adjustments without respect to the optimization goal of accuracy. In contrast, we propose a novel training framework, adaptive weighting towards two-sided fairness-aware recommendation (named Ada2Fair), which lies in the extension of the accuracy-focused objective to a controllable preference learning loss over the interaction data. Specifically, we adjust the optimization scale of an interaction sample with an adaptive weight generator, and estimate the two-sided fairness-aware weights within model training. During the training process, the recommender is trained with two-sided fairness-aware weights to boost the utility of niche providers and inactive customers in a unified way. Extensive experiments on three public datasets verify the effectiveness of Ada2Fair, which can achieve Pareto improvements in two-sided fairness-aware recommendation. Our code implementation is available at https://anonymous.4open.science/r/Ada2Fair.