Unique functionalities can arise when 2D materials are scaled down near the monolayer limit. However, in 2D materials with strong van der Waals bonds between layers, such as SnSe, maintaining stoichiometry while limiting vertical growth is difficult. Here, we describe how self-limiting stoichiometry can promote the growth of SnSe thin films deposited by molecular beam epitaxy. The Pnma phase of SnSe was stabilized over a broad range of Sn : Se flux ratios from 1 : 1 to 1 : 5. Changing the flux ratio does not affect the film stoichiometry, but influences the predominant crystallographic orientation. ReaxFF molecular dynamics (MD) simulation demonstrates that, while a mixture of Sn/Se stoichiometries forms initially, SnSe stabilizes as the cluster size evolves. The MD results further show that the excess selenium coalesces into Se clusters that weakly interact with the surface of the SnSe particles, leading to the limited stoichiometric change. Raman spectroscopy corroborates this model showing the initial formation of SnSe2 transitioning into SnSe as experimental film growth progresses. Transmission electron microscopy measurements taken on films deposited with growth rates above 0.25 Å s-1 show a thin layer of SnSe2 that disrupts the crystallographic orientation of the SnSe films. Therefore, using the conditions for self-limiting SnSe growth while avoiding the formation of SnSe2 was found to increase the lateral scale of the SnSe layers. Overall, self-limiting stoichiometry provides a promising avenue for maintaining growth of large lateral-scale SnSe for device fabrication.