  In this paper, we derive the mean-field limit of a collective dynamics model
with time-varying weights, for weight dynamics that preserve the total mass of
the system as well as indistinguishability of the agents. The limit equation is
a transport equation with source, where the (non-local) transport term
corresponds to the position dynamics, and the (non-local) source term comes
from the weight redistribution among the agents. We show existence and
uniqueness of the solution for both microscopic and macroscopic models and
introduce a new empirical measure taking into account the weights. We obtain
the convergence of the microscopic model to the macroscopic one by showing
continuity of the macroscopic solution with respect to the initial data, in the
Wasserstein and Bounded Lipschitz topologies.
