Methods and apparatus to communicate via a weld cable are disclosed. An example weld circuit communications device includes a receiver circuit, a processor, and a local communications adapter. The receiver circuit to receive a communication via a weld circuit while current is flowing through the weld circuit or after the current has stopped flowing through the weld circuit, the communication including weld voltage feedback information measured at a device remote from a power supply and remote from the weld circuit communications device while the current is flowing through the weld circuit. The processor generates power supply control information based on the weld voltage feedback information. The local communications adapter transmits the power supply control information to control welding-type power output by a power converter to regulate a weld voltage to a weld voltage setpoint.