A system for estimating the weight of a payload in a bucket of a machine is provided. The system includes a lift linkage supporting the bucket and a hydraulic lift cylinder assembly connected to the lift linkage. A pressure sensor is arranged remotely from the lift cylinder assembly. A payload measurement system is configured to monitor pressure data from the pressure sensor, hydraulic fluid temperature data and cylinder extension velocity data. The payload measurement system estimates a weight of the payload in the bucket based on the pressure data as adjusted by an estimate of a pressure drop between the lift cylinder assembly and the pressure sensor, the estimate of the pressure drop being determined based on a mathematical model that has been fitted to empirical data.