When I physically build this circuit the output voltage doesn't response to load variation.
The voltage across the sense resistor is definitely increasing when decrease the load resistance, the voltage difference between the opamp input pins varies accordingly, and there is a voltage at the output which means the NPN is turning on.
What am I missing?
R3 is way too large. Its voltage drop will hit 3.3 V at a current of just 3.3 V/50 kΩ = 66 µA, which corresponds to a load current of 100 Ω/0.1 Ω × 66 µA = 66 mA.
If you want to measure currents up to 10 A, which would be 10 mA through R3, its value can be no more than 3.3 V/10 mA = 330 Ω. In fact, it will have to be much smaller than that, because you also need to account for the voltage drops across R1 and Q1.
