Weather forecasting models are usually judged by their average skill, yet average skill says little about the rare conditions that matter most. Testing forecasts on those conditions requires a target defined consistently everywhere. Disaster catalogs record harm, but they are sparse and shaped by reporting; climatological tails can be defined everywhere, but rarity does not imply harm. We present TailWeather, a global, land-only, 0.25° dataset of climatological tail events derived from ERA5, covering 1981–2022 and early January 2023. It labels heatwaves, cold waves, heavy precipitation, and extreme wind daily, and meteorological drought monthly. Every label carries an ordinal severity tier and an intensity score relative to the local 1991–2020 climate, so users can move thresholds, within the score’s resolution, without recomputing the climatology. Compared with the EM-DAT disaster catalog, stricter tails are more strongly enriched in recorded impacts for all five hazards, by 1.6 (extreme wind) to 9.3 times (heatwave) at the best-balanced threshold. Yet 80.1 % of the world’s land population lives where the catalog is too sparse to test this link locally for at least one hazard. In forecast examples, leading AI systems that predict 2 m temperature to within about 1 K at day 1 reach a critical success index below 0.5 on heatwave tails, and their tail skill is lowest for extreme wind. TailWeather offers a reusable physical target for studying and evaluating weather extremes, one that complements rather than replaces disaster catalogs. The dataset is available at <a href="https://doi.org/10.57967/hf/10661" target="_blank" rel="noopener">https://doi.org/10.57967/hf/10661</a>.