The reason a 747 / 777 / 737 have a similar stopping distances (despite being very different weights) is to do with the number of breaking wheels each aircraft has. (The approach speeds are similar for each type). The ability to dissapate kinetic energy is the key.
A 737 has 4 breaking wheels. A 777 has 12 breaking wheels. (No idea how many a 747 has). Thus, a 777/ 747 can dissapte its energy at a similar rate to a 737. Hence the landing distances are similar.