The local moments, magnetic correlations and susceptibility in the 2D half-filled correlated Kondo lattice model are studied. We calculate their dependence on the control parameters given by local exchange coupling J _K and Coulomb repulsion U. Exact diagonalization (ED) approach for ground state properties as well as finite temperature Lanczos method (FTLM) for the uniform susceptibility are employed for small tiles on the square lattice. The competition of on-site screening and induced inter-site correlations leads to non-monotonic local moment dependence on U for weak Kondo coupling J _K . In the large U limit the numerical results are compared to those of the analytical bond operator method in mean field treatment. The variation of the Kondo temperature scale with U is obtained from the temperature dependence of the susceptibility. A monotonic increase with U is found.