  In this work we study the asymptotic behavior of the curves of the
Fu{\v{c}}{\'{\i}}k spectrum for weighted second order linear ordinary
differential equations. We prove a Weyl type asymptotic behavior of the
hyperbolic type curves in the spectrum in terms of some integrals of the
weights. We present an algorithm which computes the intersection of the
Fu{\v{c}}{\'{\i}}k spectrum with rays through the origin, and we compare their
values with the asymptotic ones.
