A turbomachine rotor balancing system including a balancing flange provided with through-passageways, and balance weights mounted fixedly on the balancing flange by at least one screw/nut assembly passing through one of the passageways is disclosed. For each of the passageways, the flange has on its first face a first recess passing via the radial summit of the passageway. This first recess being deprived of contact with the screw head pressing on this first face. The flange has on its second face a second recess passing via the radial summit. The second recess being deprived of contact with the balance weight pressing on this second face.