X-ray photoelectron spectroscopy of graphene is important both for its characterization and as a model for other carbon materials. Despite great recent interest, the intrinsic photoemission of its single layer has not been unambiguously measured, nor is the layer dependence in free-standing multilayers accurately determined. We combine scanning transmission electron microscopy and Raman spectroscopy with synchrotron-based scanning photoelectron microscopy to characterize the same areas of suspended graphene samples down to the atomic level. This allows us to assign spectral signals to regions of precisely known layer number and purity. The core level binding energy of the monolayer is measured at 284.70 eV, thus 0.28 eV higher than that of graphite, with intermediate values found for few layers. This trend is reproduced by density functional theory with or without explicit van der Waals interactions, indicating that intralayer charge rearrangement dominates, but in our model of static screening the magnitudes of the shifts are underestimated by half.