The collisional Weibel instability is investigated for a laser-ablated plasma in planar geometry. The exponential time dependence of the linear Weibel eigenmodes is obtained by numerically solving the electron Fokker-Planck and Maxwell's equations in the inhomogeneous spatial direction, with a harmonic perturbation in the transverse direction. A Cartesian tensor expansion is used to approximate the electron distribution function. Local stability analysis predicts maximum growth rates of order 1010 s-1 near the overdense side of the critical surface. The inclusion of longitudinal magnetic diffusion and electron viscosity decreases this by a factor of 5. By further including magnetic convection effects, the Weibel mode is stabilized.