When accelerated expansion of universe was discovered, the astronomers used redshift of ancient stars. Say if star is 10 billion years in the past, then it should be moving faster than star from 5 billion years ago because of distance. But not 100% faster, only close to 100% faster. So red shift for 10 bln star is slightly less than two redshifts of 5 bln year star. Is it what was measured in the discovery of accelerated cosmological expansion ?
In practice, its much more complicated than that, but you definitely have the right basic idea. Redshift vs. time is non-linear even at much lower redshifts, see this figure:
The page it comes from might also be helpful: http://www.ualberta.ca/~pogosyan/teaching/ASTRO_122/lect30a/lecture30a.html