The Voss-Weyl formula reads $$\nabla_\mu V^\mu=\frac{1}{\sqrt g}\partial_\mu(\sqrt g V^\mu),$$ where $g=\mathrm{det}( g_{\mu\nu})$. In polar plane coordinates the only non-vanishing components of the metric tensor are $g_{rr}=1$ and $g_{\theta\theta}=r^2$, so $g=r$. Then the divergence in this coordinate system as given by the above expression is $$\nabla_\mu V^\mu=\frac{1}{r}\partial_r(rV^r)+\partial_\theta V^\theta.$$
But the divergence formula in polar coordinates is the well known result $$\nabla_\mu V^\mu=\frac{1}{r}\partial_r(rV_r)+\frac{1}{r}\partial_\theta V_\theta.$$ What am I missing in the previous calculation?