Why $\frac{\Delta p}{\overline q}$ is depending by weight, flap deflection and other parameters? Which are other parameters?
The formulas deal with the relationshop between calibrated airspeed and indicated airspeed. The difference is due to two factors: 


instrument errors: these errors occur within the airspeed indicator instrument when transforming the pitot pressure to a speed indication.
position errors: these errors are caused by the position of the pitot tube on the airframe causing the pitot pressure from being different than the freestream pitot pressure.


Since the pitot tube is usually close to the fuselage of the aircraft, the local airflow around the pitot tube is influenced by the aerodynamic properties of the aircraft itselfs. The pitot tube's location is chosen such the the local flow characteristics deviate as little as possible from the freestream characteristics but there will be a measurable difference in pressure between the freestream total pressure and the pitot pressure. The pressure differences depends on airflow around the aircraft which is infuenced by the angle of attack (and thus weight) flaps, slats, gear, turn rate, side slip angle etc. 

In order to analyse the position errors during a flight test programme, test aircraft are often fitted with additional pitot probes protruding ahead the airframe and/or trailing cones (for static pressure measurement) far behind the aircraft.