  In this paper, we prove a classification for complete embedded constant
weighted mean curvature hypersurfaces $\Sigma\subset\mathbb{R}^{n+1}$. We
characterize the hyperplanes and generalized round cylinders by using an
intrinsic property on the norm of the second fundamental form. Furthermore, we
prove an equivalence of properness, finite weighted volume and exponential
volume growth for submanifolds with weighted mean curvature of at most linear
growth.
