Installing additional weapons on a plane in World of Warplanes will affect its flying qualities to a greater or lesser extent. The main characteristics this will affect are agility and speed. You can see the difference in performance of an aircraft directly in the menu «Modules» in the hangar.
If you select a module you can also see the performance statistics of a plane increase or decrease in the side window.
Typically, an aircraft’s performance characteristics are most heavily affected by outboard cannons, bombs and rockets. However, once the bombs and rockets are used in combat, your planes speed and manoeuvrability will increase. Additionally, large-calibre guns affect the flight performance of the aircraft to a bigger degree.