Finite-size effects on the gravitational wave signal from a neutron star merger typically manifest at high frequencies where detector sensitivity decreases. Proposed sensitivity improvements can give us access both to stronger signals and to a myriad of weak signals from cosmological distances. The latter will outnumber the former and the relevant part of the signal will be redshifted towards the detector's most sensitive band. We study the redshift dependence of information about neutron star matter and find that single-scale properties, such as the star radius or the postmerger frequency, are better measured from the distant weak sources from z∼1.