  We obtain order sharp spectral estimates for the difference of resolvents of
singularly perturbed elliptic operators $\mathbf{A}+\mathbf{V}_1$ and
$\mathbf{A}+\mathbf{V}_2$ in a domain $\Omega\subseteq \mathbb{R}^\mathbf{N}$
with perturbations $\mathbf{V}_1, \mathbf{V}_2$ generated by $V_1\mu,V_2\mu,$
where $\mu$ is a measure singular with respect to the Lebesgue measure and
satisfying two-sided or one-sided conditions of Ahlfors type, while $V_1,V_2$
are weight functions subject to some integral conditions. As an important
special case, spectral estimates for the difference of resolvents of two Robin
realizations of the operator $\mathbf{A}$ with different weight functions are
obtained. For the case when the support of the measure is a compact Lipschitz
hypersurface in $\Omega$ or, more generally, a rectifiable set of Hau{\ss}dorff
dimension $d=\mathbf{N}-1$, the Weyl type asymptotics for eigenvalues is
justified.
