A payload weight of a load of material carried by an implement of a machine may be estimated taking into account angular acceleration of the payload. A lift cylinder pressure differential and a lift arm angular acceleration may be determined as the implement is raised through a weigh range. An angular acceleration compensation factor may be determined from the lift arm angular acceleration, and a compensated differential pressure may be calculated by multiplying the lift cylinder pressure differential by the angular acceleration compensation factor. The estimated payload weight may then be determined based on the compensated pressure differential and a head end cross-sectional area of the lift cylinder.