At the street racing scene, the one where Ghost Jr (Nick Tse) had to enter to gain an entry into the gang that he was infiltrating. After the cars had started, I noticed that all cars at the front including the Skyline of Ghost Jr, the Silvia S14 and the S13 180SX that he raced against braked heavily to allow the smaller cars (Integra Type-R, MRS) pass.
What is the reason behind that and why would they allow them to pass
Depends on if they knew the route. Sometimes it's easier to let the small cars pass for early sharp or narrow corners to avoid being bumped, spinned or cluttered up ahead which later happens. A good driver will sometimes let a slower vehicle get in the lead at the early part of the race if it's a tricky course and pass them at convenience later (which the Skyline and Silva could easily do on the straightaways).
But that's just a guess, they obviously aren't professionals and the effect itself could have just been for movie purposes.