For many 2D materials, optical and Raman spectra are richly structured, and convey information on a range of parameters including nanosheet size and defect content. By contrast, the equivalent spectra for h-BN are relatively simple, with both the absorption and Raman spectra consisting of a single feature each, disclosing relatively little information. Here, the ability to size-select liquid-exfoliated h-BN nanosheets has allowed us to comprehensively study the dependence of h-BN optical spectra on nanosheet dimensions. We find the optical extinction coefficient spectrum to vary systematically with nanosheet lateral size due to the presence of light scattering. Conversely, once light scattering has been decoupled to give the optical absorbance spectra, we find the size dependence to be mostly removed save for a weak but well-defined variation in energy of peak absorbance with nanosheet thickness. This finding is corroborated by theoretical calculations. In addition, while we find the position of the sole h-BN Raman line to be invariant with nanosheet dimensions, the linewidth appears to vary weakly with nanosheet thickness. These size-dependent spectroscopic properties can be used as metrics to estimate nanosheet thickness from spectroscopic data.