Reanalysis of the photoassociation spectrum of the weakly binding (6S1/2 + 6P3/2) lg 133Cs2 levels, reported in the previous study [J. Mol. Spectro. 255 (2009) 106], is performed by using a Lu-Fano graph coupled to the improved LeRoy- Bernstein formula including two additional modified terms. A more accurate coefficient (c3) is obtained for the leading long-range potential (-c3/R3) of a diatomic molecule.