The elastic scattering angular distributions of the weakly bound 9Be projectile from 208Pb and 209Bi have been measured for 14 beam energies near the threshold from 37 to 50 MeV. The parameters of the optical potential are extracted by means of phenomenological optical model analysis with PTOLEMY. Both of the systems show unusual potential behavior in the vicinity of the Coulomb barrier that the strength of the imaginary (absorptive) part of the potential is increasing (rather than decreasing) with decreasing energy, which is quite different from the results of some previous reports. This unusual threshold phenomenon indicates that the breakup channel is strongly coupled with the elastic channel and has obvious effects on the optical potential. The analyses also show that high precision elastic scattering angular distributions, especially those below the Coulomb barrier, are very important for extracting correct threshold behavior of the optical potential.