Decision-making in ship weather routing heavily relies on weather forecasts, but the inherent uncertainties in their predictions still remain a challenge. This study focuses on quantifying the uncertainty of weather forecasts over a considerable period of time for the North Atlantic Ocean area to enable their integration into ship routing systems. A comprehensive analysis of the collected weather data is presented, systematically accounting for the propagating forecast uncertainties. The proposed framework models forecast variability through probabilistic distributions of several relevant weather variables, such as wind speed and wave height, taking into account the degradation of forecast accuracy over time. For each chosen variable, uncertainty bounds and confidence intervals are estimated over different time horizons. These metrics are used as actionable insights that can potentially be integrated into on-board decision support systems. Ship weather routing often involves conflicting objectives, which further highlights the limitations of deterministic decision support systems as well. Adaptive adjustments to route planning must be considered in response to evolving weather conditions along the ship's route. A method for embedding the forecast uncertainty into optimization decision variables, including course and speed changes, to balance operational goals such as safety, efficiency and environmental impact is presented. To support the integration of raw weather forecast data with the operational needs of the vessel, this research provides the basis for better routing decisions. Incorporating weather forecast uncertainties into decision support tools allows them to identify routes that remain stable under realistic conditions.