A greater stopping distance especially in emergency situationsis:-
The kinetic energy of an object is directly proportional to the object’s mass.
KE = 1/2 mv^2
Any increase in mass due to load will increase the kinetic energy. Brakes work by dissipating the KE, converting it to heat. More KE needs more heat, and that means you have to keep the brake on longer.
You can dissipate the KR in a shorter braking distance if you use bigger brake pads and if you use wider tires.
But the same car with an added load will have a greater braking distance. That’s physics.