  Let $K$ be a field. We characterise the row-finite weighted graphs $(E,w)$
such that the weighted Leavitt path algebra $L_K(E,w)$ is isomorphic to an
unweighted Leavitt path algebra. Moreover, we prove that if $L_K(E,w)$ is
locally finite, or Noetherian, or Artinian, or von Neumann regular, or has
finite Gelfand-Kirillov dimension, then $L_K(E,w)$ is isomorphic to an
unweighted Leavitt path algebra.
