I would suggest that if the downward force on the towing vehicles rear wheels was increased the friction with the road would be increased. This would help with traction and reducing the chance of the wheels slipping. Therefore, more downward stopping force.
However, this extra friction would probably be negated by the fact that the total mass of the car and trailer would increase the forward momentum, which would take more time and distance to stop.
'If you apply your logic you are saying that a heavier mass will stop quicker. This does defy the laws of physics and what you are suggesting is that a Juggernaut could stop quicker than a small car. I'm not convinced'
If you increase mass it will of course travel further when resistance is applied unless increased resistance is used. A small car has only 4 wheels (2 axles) Probably 3/4 of the braking efficiency is on the front axle. A lorry has many axles. Provided the load is correctly distributed (which is why police check axle weights) it is conceivable that it will stop in a shorter distance from similar speeds. However their is a caviat to this as airbrakes require time (1/2 second) to build up pressure and move the brake actuators
To quote Wikipedia Braking distance refers to the distance a vehicle will travel from the point where its brakes are fully applied to when it comes to a complete stop. It is affected by the original speed of the vehicle, the type of brake system in use, the reaction time of the driver/rider and the coefficient of friction between its tires and the road surface.