  We demonstrate broadband tuning of an optomechanical microcavity optical
resonance by exploring the large optomechanical coupling of a double-wheel
microcavity and its uniquely low mechanical stiffness. Using a pump laser with
only 13 mW at telecom wavelengths we show tuning of the silicon nitride
microcavity resonances over 32 nm. This corresponds to a tuning power
efficiency of only 400 $\mu$W/nm. By choosing a relatively low optical Q
resonance ($\approx$18,000) we prevent the cavity from reaching the regime of
regenerative optomechanical oscillations. The static mechanical displacement
induced by optical gradient forces is estimated to be as large as 60 nm.
