This paper presents the β-decay feeding intensity distribution and Gamow-Teller transition strength distribution of 71,73Ni. These quantities were measured using the technique of total absorption spectroscopy at the National Superconducting Cyclotron Laboratory with the Summing NaI(Tl) detector. These measurements provide sensitive constraints to theoretical models used to predict β-decay properties far from stability for astrophysical applications. Specifically, for the astrophysical r process, the majority of the involved nuclei are not accessible by current facilities, and the nuclear input is mainly provided by theory. The present work reports on two neutron-rich nickel isotopes in the region where the weak r process is expected to be relevant in stellar nucleosynthesis. The experimental results are compared to two theoretical models, namely the shell model and the quasiparticle random-phase approximation, to help further refine theoretical calculations and aid in future r-process studies.