Structure of planar cholesteric cells under weak anchoring conditions has been considered from both theoretical and experimental point of view. Director distribution of the cell has been calculated in the frame of continuum theory, taking into account boundary conditions. Solutions are discussed with respect to anchoring energy, cell thickness and unperturbed cholesteric pitch. Considering a wedged cholesteric sample where planar weak anchoring is assumed at both interfaces, it is shown that two regimes exist: lined with Grandjean-Cano defects at high thicknesses and free of lines at low thicknesses. In such a wedge, the number of “missing” lines depends on anchoring energy, twist elastic constant and unperturbed cholesteric pitch. The position of the existing lines differs from that they have under strong anchoring conditions, the equidistance is lost. Experimental evidence of these two regimes is also reported.