What does a spring scale read when two equal weights are hung from a pulley system?

The spring scale reads the tension in the rope, which equals the weight of one mass (mg), not the sum of both weights. For two 100N weights the scale reads 100N not 200N.

Why doesn't the scale read 200N with two 100N weights?

Because tension in a continuous frictionless rope is constant throughout. The scale measures the tension which is the same force that supports each weight individually. It is like standing on a bathroom scale — the scale reads your weight not your weight plus the floor's reaction force.

Pulley-Spring Scale System — Why Doesn't th...

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Pulley–Spring Scale System