Critical adsorption for weak surface field h(1) is reconsidered. On the basis of physical heuristic arguments, approximate behavior of the scaling function is derived. New form of a scaling for weak h(1) in finite systems is proposed and verified by testing against exact results obtained for this purpose in the 2D Ising strips, For weak h(1) we find the approximate behavior of adsorption Gamma similar to tau(beta-Delta 1) for the reduced temperatures h(1)(1/Delta 1)similar to tau much less than 1. This behavior is consistent with experimental data [N. S. Desai, S. Peach, and C. Franck, Phys. Rev. E 52, 4129 (1995)] obtained for tau=10(-5), and is in a very good agreement with exact results in the 2D Ising strip.