Superconducting circuit technology has rapidly developed over the past several years to become a leading contender for realizing a scalable quantum computer. Modern circuit designs are based on the transmon qubit, which coherently superposes macroscopic charge oscillations. Measurements of a transmon are fundamentally weak and continuous in time, with projective measurements emerging only after a finite duration. Adding gates, such measurements may then implement ancilla-based measurements of controllable strength. Recent experiments have used both types of weak measurement to great effect: for monitoring qubit evolution, and for showing violations of a hybrid Bell-Leggett-Garg inequality.