We consider two models which lead to the prediction of a weight change of gyroscopes depending on the rate of rotation: mass-energy equivalence and Weber's force for gravitation. We calculate the order of magnitude of this effect in both models and show that Weber's model predicts a weight change depending on the spin axis orientation resembling close similarities to observed Earth flyby anomalies. However, our predicted effect is much smaller than the observed effect, which could explain why flyby anomalies were not detected anymore in recent spacecraft trajectories.5 176179