The spring balance in the picture is calibrated to measure force -- the tension in the cord.
The magnitude of the upward pull by the cord must exactly cancel the downward pull of gravity, so the magnitude of the tension in the bungee cord is the same as the weight of the man. We often call the scale reading “the weight”, but really it’s the tension.
How much does a 100 kg man weigh?
The spring scale touches only the cord and so measures only the tension in the cord. It is Newton’s three laws of motion that convince us that the reading on the spring scale is just the magnitude of the weight of the man.