We succeeded in controlling the measurement strength of a macroscopic quantum system, namely a persistent current quantum bit (qubit), by using a transmission line type Josephson bifurcation amplifier (JBA: an ac-driven superconducting quantum interferometer device) as a probe. By employing a special pulse sequence, we found that the weighted average of the Ramsey fringe visibility (α-value) can be used as an indicator of quantum state projection. The sudden change in the α-value magnitude at around the threshold suggests that an entangled state of the qubit–JBA composite system settles in one of the two possible classically correlated qubit–JBA states caused by strong decoherence. This is an important result in terms of understanding the mechanisms of quantum state measurement.