The frictional force of your tires depends on their coefficient of friction and the normal force of the car (essentially how heavy it is).
F_f=\mu*F_n
with mu being the coefficient of friction.
F=ma
The frictional force is proportional to the mass of the car. The effect of frictional force (acceleration) is inversely proportional to the mass of the car.
That is close enough to provide a decent estimate under practical conditions, hence everyone learning the same basic rules for how many car lengths to leave between you and the car in front of you. The rule you learn is primarily based on reaction time, since all cars and trucks will have roughly the same stopping distance.
In an ideal world where every car puts on their brakes at exactly the same time, panic stopping on the highway would be as graceful as a ballet.
Obviously, not all tires have exactly the same coefficient of friction. For one thing you may have new tires and the person behind you may have threads beginning to protrude from their tires. And the coefficient of friction of your tires will vary based on how much air is in the tires, load conditions, etc.
And the coefficient of friction can change based on the weather (hot, cold, wet, dry). Everyone on the road will experience the same weather conditions, but, because their tires are different, the weather won't affect everyone's tires quite the same.
And, of course, at least a few people will be driving with brakes in various states of repair.
So the simple scenario, that stopping distance relies solely on speed and reaction time (and not mass), is only a rough estimate, but one that works reasonably well, provided the rough estimate is conservative enough to take in most variations in stopping ability you're likely to see on the highway.
While not relevant for most highway conditions, overheating your brakes can be a fatal mistake when driving through the mountains. We have a big mountain (Pikes Peak) just outside the city. Every few years or so, we'll get a tourist that ignores the signs telling them to use a lower gear, finds a way to avoid the 'mandatory' brake test (officials literally measure the temperature of your brakes), and then the next day, the newspaper has stories from eye witnesses describing the terrified look of the poor kids in the back seat as their dad tried to navigate the mountain with no brakes. The newspaper rarely has any eyewitness reports from the vehicle's occupants, as they usually die.