We report detailed experimental results of magnetic susceptibility for the La0.5RE0.5BaCaCu3O7-delta superconducting system, above and close the superconducting transition. The data were obtained from 5 K up to 300 K, and applied field of 0.1 T, correspond to the so-called weak magnetic field limit. In this limit, the excess of magnetization is associated with the fluctuations of the vortex lines positions. These effects of thermal fluctuations on M-ab can be quantified through the known "excess of diamagnetism" Delta chi(ab), but TTC.In this work we present a study of magnetic susceptibility fluctuations in the limit of weak magnetic fields, above the La0.5RE0.5BaCaCu3O7-delta (RE=Y, Sm, Gd, Dy, Ho, Yb) high superconducting material. Samples were synthesized by the standard solid state reaction. The best adjustment in the experimental data, in the limit of weak magnetic field, of Delta chi/T in function of the reduced temperature allowed to obtain the values of A(S) (diamagnetism of Schmidt) and B-LD (parameter LD), in each one of the samples of the systems La0.5RE0.5BaCaCu3O7-delta. For the fluctuation analysis, we use the concept of excess of magnetization, based on the Lawrence-Doniach model (LD), which allowed to calculate the diamagnetism induced by thermal fluctuations in the normal state, in the vicinities of critical temperature T-c0 (74, 58, 74, 55, 60, 46 K, for RE=Y, Sm, Gd, Dy, Ho, Yb respectively). It was demonstrated, by means of the analysis of the thermal fluctuations, that the La0.5RE0.5BaCaCu3O7-delta system shows an excellent 2D scaling behavior (B-LD).