An agricultural harvesting head for an agricultural harvester has a constant force assembly that changes the mechanical advantage of a spring applied to the mainframe of the agricultural harvesting head. As the mainframe of the agricultural harvesting head moves up and down on the front of the combine feederhouse, compressing and decompressing the spring, the constant force assembly changes the mechanical advantage of the spring such that the spring provides a relatively constant lifting force to the mainframe of the harvesting head as the mainframe moves up and down.