We present a simple, continuous, cavity-enhanced optical absorption measurement technique based on high-bandwidth Pound-Drever-Hall (PDH) sideband locking. The technique provides a resonant amplitude quadrature readout that can be mapped onto the cavity's internal loss rate and is naturally compatible with weak probe beams. With a proof-of-concept 5-cm-long Fabry-Perot cavity, we measure an absorption sensitivity ∼10-10cm-1/Hz from 30 kHz to 1 MHz, and a minimum value of 6.6×10-11cm-1/Hz at 100 kHz, with 38 µW collected from the cavity's circulating power.