In the wire & cable business, the device you describe is called a dancer, for the way its components move about while regulating the tension in a rope or wire being unspooled from a large coil.
The simplest examples use a rim brake which drags against the flange on the big spool. The rim brake is on a lever arm and the end of the arm is attached to a coil spring. That coil spring in turn is attached to a pulley through which the wire is routed.
Tugging on the end of the wire pulls the pulley, which pulls the spring, which pulls the lever, which pulls the brake shoe out of contact with the spool rim and allows the spool to turn and thereby feed wire off it. Letting go of the end of the wire releases the spring tension and allows the brake shoe to come back into contact with the spool, stopping it and thereby maintaining tension on the wire so it doesn't go slack and unwrap itself from the spool and create a tangle.
Spooling tensioners usually have a DC electric motor drive connected to the spool and a spring-and-pulley device which operates on the speed control knob for the DC motor. When you turn on the spooler, the motor comes on and begins rotating the spool which then pulls on the wire. as the tension in the wire climbs, the pulley shifts position, the spring deflects, and the tension control knob is turned down. When wire is then fed into the pulley, the spring tension is released and the tension control is turned up and the DC motor begins rotating the spool which takes up the wire.
The simplest upspooling tensioners have no mechanical control means at all; you simply adjust the current being fed to the upspool motor which sets its torque output at stall and you then feed in your wire. The motor runs until the tension starts going up in the wire, which causes the current flow up go up until the current limit is met at which point the motor stalls and the wire infeed halts at the desired tension.
