We present a nanofluidic optical device based on light-scattering microscopy, which enables label-free detection and quantitative analysis of individual biomolecules freely moving in solution. The key component is a nanochannel with subwavelength dimensions, which is imaged by dark-field microscopy. Due to interference between light scattered by the nanochannel and a biomolecule inside it, a single biomolecule can be directly detected. In addition, the molecular weight can be measured, both by tracking the Brownian motion and from the optical contrast. This is demonstrated for both single DNAs and proteins with molecular weights ranging down to tens of kDa.