  We consider a system of infinitely many interacting Brownian motions that
models the height of a one-dimensional interface between two bulk phases. We
prove that the large scale fluctuations of the system are well approximated by
the solution to the KPZ equation provided the microscopic interaction is weakly
asymmetric. The proof is based on the martingale solutions of Goncalves and
Jara and the corresponding uniqueness result of Gubinelli and Perkowski.
