The prevalence of chronic stress represents a major public health concern, yet automated detection of vulnerable individuals remains limited. Social media platforms like X (formerly Twitter) serve as important venues for people to share their experiences openly. This paper introduces StressRoBERTa, a cross-condition transfer learning approach for the automatic detection of self-reported chronic stress in English tweets. We investigate whether continual pretraining on clinically related conditions, such as depression, anxiety, and PTSD, which have a high comorbidity with chronic stress, improves stress detection compared to general language models. We continually pretrained RoBERTa on the Stress-SMHD corpus, a subset of Self-reported Mental Health Diagnoses focused on stress-related conditions, consisting of 108 million words from users with self-reported diagnoses of depression, anxiety, and PTSD. Then, we fine-tuned on the SMM4H 2022 Shared Task 8. StressRoBERTa achieves 82% F1, which outperforms the best shared task system (79% F1) by 3 percentage points. Our results demonstrate that focused cross-condition transfer learning from stress-related disorders provides stronger representations than general mental health training. To validate cross-condition generalization, we also fine-tuned the model on the Dreaddit. Our result of 81% F1 further demonstrates the transfer from clinical mental health contexts to situational stress discussions.