Insufficient data and lack of labeled data are common issues in state-of-health (SOH) estimation of Lithium-Ion battery. Federated learning-based SOH estimation methods offer a promising solution by collaborating multiple battery users to train the SOH estimation model while protecting data privacy. However, existing federated learning-based methods assume that the data collected by local clients are labeled. In practical applications, the labeled data is often sparse due to the high cost of testing battery capacity. To address this problem, a dynamic weighted federated contrastive self-supervised learning method (DW-FCSSL) is proposed in this paper. This approach leverages distributed unlabeled datasets to jointly train a global feature extractor across multiple clients while protecting data privacy, and is subsequently applied to battery SOH estimation. In particular, a time-frequency mixing based data augmentation (TFM-Aug) method is firstly proposed to enhance the capability for feature self-extraction. Secondly, an additional time information reconstruction module is incorporated into intra-client and client-server contrastive learning to extract multi-level degradation information of batteries from scattered unlabeled data. Further, a process-aware dynamic weighted aggregation algorithm is proposed to mitigate the effect of low-quality data from local client on the global model. With the trained global feature extractor, only a small number of labeled samples are required for each client to train a personalized estimator. Finally, the SOH estimation performance of DW-FCSSL is validated on the self-collected battery dataset and NASA battery dataset. It achieves a statistic estimation error of 2.80 % on the self-collected battery dataset with only 20 % labeled samples.