Climate-optimized routing is an operational measure to effectively reduce the climate impact of aviation with a slight increase in aircraft operating costs. This study examined variations in the flight characteristics among five aircraft routing strategies and discusses several characteristics of those routing strategies concerning typical weather conditions over the North Atlantic. The daily variability in the North Atlantic weather patterns was analyzed by using the European Center Hamburg general circulation model (ECHAM) and the Modular Earth Submodel System (MESSy) Atmospheric Chemistry (EMAC) model in the specified dynamics mode from December 2008 to August 2018. All days of the ten complete winters and summers in the simulations were classified into five weather types for winter and into three types for summer. The obtained frequency for each of the weather types was in good agreement with the literature data; and then representative days for each weather type were selected. Moreover, a total of 103 North Atlantic flights of an Airbus A330 aircraft were simulated with five aircraft routing strategies for each representative day by using the EMAC model with the air traffic simulation submodel AirTraf. For every weather type, climate-optimized routing shows the lowest climate impact, at which a trade-off exists between the operating costs and the climate impact. Cost-optimized routing lies between the time- and fuel-optimized routings and achieves the lowest operating costs by taking the best compromise between flight time and fuel use. The aircraft routing for contrail avoidance shows the second lowest climate impact; however, this routing causes extra operating costs. Our methodology could be extended to statistical analysis based on long-term simulations to clarify the relationship between the aircraft routing characteristics and weather conditions.