Background: Existing studies mainly focus on the relationship between real-time weather and traffic crash injury severity, while few scholars have investigated the operation risk levels caused by traffic incidents. Identifying weather-related factors that affect the incident-induced delay is helpful for estimating the delay levels when an incident occurs. Accordingly, the present study profoundly explores the relationship between weather conditions and traffic delays caused by traffic incidents. Methods: The traffic incident and weather datasets from January 1 to December 31, 2020, in New York State are used. To that end, the hazard-based duration and multinomial logit modeling frameworks are employed to determine the effect of weather conditions on the duration of traffic delay and the delay severity, respectively. More importantly, to account for multiple layers of unobserved heterogeneity, a random parameter with heterogeneity in means approach is introduced into the above two models. Results: (1) The strong breeze (wind speed over 8 m/s) and low visibility (visibility under 5 km) significantly affect the duration of delay. (2) Hot day (between 20 and 30 °C) has a 344.03 % greater probability of minor delay. A strong breeze has a higher probability of severe delay. The low visibility is found to increase the estimated odds of moderate delay and severe delay by 51.15 % and 13.39 %, respectively. In comparison, the normal visibility (between 10 and 20 km) significantly decreases the estimated odds of severe delay by 119.17 %. Conclusions: Compared with other weather factors, wind speed, temperature, and visibility have the greatest impact on the traffic delay levels after a traffic accident, and there are significant differences in the impact under different delay severity. Findings from this study will help policymakers to establish comprehensive differentiating security measures to resolve traffic delays.