As large language models continue to advance, ensuring their trustworthiness is critical. However, inaccessible real-world ground truth labels pose a significant challenge in high-stakes domains. Recent studies have highlighted weak-to-strong generalization, where a strong model trained only on a weak model's labels surpasses the weak model in task performance. Yet, whether critical trustworthiness properties such as robustness, fairness, and privacy can generalize similarly remains an open question. This is the first work to study this question by examining if a stronger model can enhance trustworthiness when fine-tuned on a weaker model’s labels, a paradigm we term weak-to-strong trustworthiness. To address this, we introduce two fundamental fine-tuning strategies that leverage trustworthiness regularization during the fine-tuning of the weak and weak-to-strong models. Our experimental evaluation on real-world datasets reveals that while some trustworthiness properties, such as fairness, adversarial, and OOD robustness, show significant improvement in trustworthiness generalization when both models were regularized, others like privacy do not exhibit signs of weak-to-strong trustworthiness. Our results highlight the potential of weak-to-strong trustworthiness as a practical pathway for enhancing the trustworthiness of increasingly capable AI systems, even under imperfect real-world conditions.