Accurate assessments of extreme weather events are vital for research and policy, yet localized and granular data remain scarce in many parts of the world. This data gap limits our ability to analyze potential outcomes and implications of extreme weather events, hindering effective decision-making. Large Language Models (LLMs) can process vast amounts of unstructured text data, extract meaningful insights, and generate detailed assessments by synthesizing information from multiple sources. Furthermore, LLMs can seamlessly transfer their general language understanding to smaller models, enabling these models to retain key knowledge while being fine-tuned for specific tasks. In this paper, we propose Extreme Weather Reasoning-Aware Alignment (EWRA), a method that enhances small language models (SLMs) by incorporating structured reasoning paths derived from LLMs, and ExtremeWeatherNews, a large dataset of extreme weather event-related news articles. EWRA and ExtremeWeatherNews together form the overall framework, ClimaEmpact, that focuses on addressing three critical extreme-weather tasks: categorization of tangible vulnerabilities/impacts, topic labeling, and emotion analysis. By aligning SLMs with advanced reasoning strategies on ExtremeWeatherNews (and its derived dataset ExtremeAlign used specifically for SLM alignment), EWRA improves the SLMs' ability to generate well-grounded and domain-specific responses for extreme weather analytics. Our results show that the approach proposed guides SLMs to output domain-aligned responses, surpassing the performance of task-specific models and offering enhanced real-world applicability for extreme weather analytics.