I've done a bit of science, which will probably have to be redone with the upcoming rollers tweak.
I built a track to test how far a cart goes when pushed by a dwarf, and when rollers are added:
This is with 20 rollers, showing the cart's final position at 444 tiles traveled.
DATA:
Dwarf push (no rollers) : 123 tiles A cart pushed by a dwarf always goes 123 tiles, whether empty, full of rocks, or with a SPEED:1 dwarf.
Dwarf push and 1 roller (highest speed) : 166 tiles
Dwarf push and 2 rollers (highest speed) : 226 tiles
Dwarf push and 3 rollers (highest speed) : 238 tiles
Dwarf push and 4 rollers (highest speed) : 257 tiles
Dwarf push and 5 rollers (highest speed) : 270 tiles
Dwarf push and 10 rollers (highest speed) : 430 tiles
Dwarf push and 20 rollers (highest speed) : 444 tiles
Dwarf push and 1 roller (lowest speed) : 123 tiles
Dwarf push and 5 rollers (lowest speed) : 123 tiles
Dwarf push and 1 roller (low speed) : 155 tiles
Dwarf push and 5 rollers (low speed) : 155 tiles
Dwarf push and 1 roller (medium speed) : 166 tiles
Dwarf push and 5 rollers (medium speed) : 218 tiles
Dwarf push and 1 roller (high speed) : 166 tiles
Dwarf push and 5 rollers (high speed) : 276 tiles
It seems weight and dwarf speed make no difference in travel distance. It tried vanilla, SPEED:1, empty, and loaded with rocks. No observable difference when pushed. Rollers seem to work weirdly. Adding 1 highest speed roller adds 43 tiles traveled, adding another adds 60, another adds 12, another adds 19, another adds 33.