  Type Ia supernovae (SNe Ia) are used as standardisable candles to measure
cosmological distances, but differences remain in their corrected luminosities
which display a magnitude step as a function of host galaxy properties such as
stellar mass and rest-frame $U-R$ colour. Identifying the cause of these steps
is key to cosmological analyses and provides insight into SN physics. Here we
investigate the effects of SN progenitor ages on their light curve properties
using a galaxy-based forward model that we compare to the Dark Energy Survey
5-year SN Ia sample. We trace SN Ia progenitors through time and draw their
light-curve width parameters from a bimodal distribution according to their
age. We find that an intrinsic luminosity difference between SNe of different
ages cannot explain the observed trend between step size and SN colour. The
data split by stellar mass are better reproduced by following recent work
implementing a step in total-to-selective dust extinction ratio $(R_V)$ between
low- and high-mass hosts, although an additional intrinsic luminosity step is
still required to explain the data split by host galaxy $U-R$. Modelling the
$R_V$ step as a function of galaxy age provides a better match overall.
Additional age vs. luminosity steps marginally improve the match to the data,
although most of the step is absorbed by the width vs. luminosity coefficient
$\alpha$. Furthermore, we find no evidence that $\alpha$ varies with SN age.
