  Measurements are crucial in quantum mechanics, in fundamental research as
well as in applicative fields like quantum metrology, quantum-enhanced
measurements and other quantum technologies. In the recent years,
weak-interaction-based protocols like Weak Measurements and Protective
Measurements have been experimentally realized, showing peculiar features
leading to surprising advantages in several different applications. In this
work we analyze the validity range for such measurement protocols, that is, how
the interaction strength affects the weak value extraction, by measuring
different polarization weak values measured on heralded single photons. We show
that, even in the weak interaction regime, the coupling intensity limits the
range of weak values achievable, putting a threshold on the signal
amplification effect exploited in many weak measurement based experiments.
