We study surface-enhanced Raman scattering (SERS) of individual organic molecules embedded in dimers of two metal nanoparticles. The good control of the dimer preparation process, based on the usage of bifunctional molecules, enables us to study quantitatively the effect of the nanoparticle size on the SERS intensity and spectrum at the single molecule level. We find that as the nanoparticle size increases the total Raman intensity increases and the lower energy Raman modes become dominant. We perform an electromagnetic calculation of the Raman enhancement and show that this behavior can be understood in terms of the overlap between the plasmonic modes of the dimer structure and the Raman spectrum. As the nanoparticle size increases, the plasmonic dipolar mode shifts to longer wavelength and thereby its overlap with the Raman spectrum changes. This suggests that the dimer structure can provide an external control of the emission properties of a single molecule. Indeed, clear and systematic differences are observed between Raman spectra of individual molecules adsorbed on small versus large particles.