By using the new experimental data of AA potential, this paper has performed a full calculation for strange hadronic matter with different strangeness contents as well as its consequences on the global properties of neutron star matter in relativistic mean field model. It finds that the new weak hyperon-hyperon interaction makes the equations of state much stiffer than the result of the previous strong hyperon-hyperon interaction, and even stiffer than the result without consideration of hyperon-hyperon interaction. This new hyperon-hyperon interaction results in a maximum massof 1.75M⊙ (where M⊙ stands for the mass of the Sun), about 0.2-0.5M⊙ larger than the previous prediction with the presence of hyperons. After examining carefully the onset densities of kaon condensation it finds that this new weak version of hyperon-hyperon interaction favours the occurrence of kaons in comparison with the strong one.