Sintering of nanoparticle inks over large area-substrates is a key enabler for scalable fabrication of patterned and continuous films, with multiple emerging applications. The high speed and ambient condition operation of photonic sintering has elicited significant interest for this purpose. In this work, we experimentally characterize the temperature evolution and densification in photonic sintering of silver nanoparticle inks, as a function of nanoparticle size. It is shown that smaller nanoparticles result in faster densification, with lower temperatures during sintering, as compared to larger nanoparticles. Further, high densification can be achieved even without nanoparticle melting. Electromagnetic Finite Element Analysis of photonic heating is coupled to an analytical sintering model, to examine the role of interparticle neck growth in photonic sintering. It is shown that photonic sintering is an inherently self-damping process, i.e., the progress of densification reduces the magnitude of subsequent photonic heating even before full density is reached. By accounting for this phenomenon, the developed coupled model better captures the experimentally observed sintering temperature and densification as compared to conventional photonic sintering models. Further, this model is used to uncover the reason behind the experimentally observed increase in densification with increasing weight ratio of smaller to larger nanoparticles.