  In this paper we investigate the origin of the Balanced Viscosity solution
concept for rate-independent evolution in the setting of a finite-dimensional
space. Namely, given a family of dissipation potentials $(\Psi_n)_n$ with
superlinear growth at infinity and a smooth energy functional $\mathcal{E}$, we
enucleate sufficient conditions on them ensuring that the associated gradient
systems $(\Psi_n,\mathcal{E})$ Evolutionary Gamma-converge to a limiting
rate-independent system, understood in the sense of Balanced Viscosity
solutions. In particular, our analysis encompasses both the vanishing-viscosity
approximation of rate-independent systems and their stochastic derivation.
