A vibration dampening system for a motor shaft in an electric submersible pump ESP uses axially extending arms in one or opposed directions from a fixed portion of a motor shaft bearing. The weights can have their location adjusted to tune the device to the natural frequencies of the rotating shaft and to add an ability to address vibration in more than one plane. Openings are provided in the support for the arms that hold the weight so that arm vibration can create turbulence and improve heat dissipation in the oil for improved bearing life. Bearing cost can be reduced using more economical materials without sacrificing bearing life.