The paper investigates resonant nonlinear Neumann problems driven by the \(p\)-Laplacian plus an indefinite potential. First, the spectral properties of this operator are investigated. Then, there are given several multiplicity results which allow to have resonance with respect to the operator in the principal part. A basic feature of these results is that the weight can be unbounded. The results become sharper in the semilinear case. The approach is based on variational methods, truncation techniques and Morse theory.