Weak approximate implicitization is a method for finding an algebraic hypersurface q(x) = 0 approximating a parametrically represented manifold p(s) by minimizing the integral \smallint \Omega(q(p(s)))^2 ds. We show that the properties of the original approach to approximate implicitization, such as the high convergence rates and the approximation of multiple manifolds, are inherited by weak approximate implicitization. While the computational speed of weak approximate implicitization is better than for the original approach, the rounding errors are slightly larger.