In this work we study the homogenisation problem for nonlinear elliptic equations involving$p$-Laplacian-type operators with sign-changing weights. We study the asymptotic behaviour of variational eigenvalues which consist of a double sequence of eigenvalues. We show that the$k$th positive eigenvalue goes to infinity when the average of the weights is nonpositive, and converges to the$k$th variational eigenvalue of the limit problem when the average is positive for any$k\geq 1$.