Damping and spin transport in spintronic multilayered systems continues to be a topic of active research. The enhancement of damping in ferromagnet(FM)/spacer layer (SL)/heavy metal (HM) thin-film systems was studied for Co25Fe75/SL/Pt with a non-magnetic (NM) SL of either Au or Cu with variable thickness, in order to understand the correlation with proximity induced magnetism (PIM) in the HM. Structural, PIM and magnetic damping measurements were undertaken on the same samples. Specifically, secondary ion mass spectroscopy (SIMS), element specific X-ray magnetic reflectivity and X-ray magnetic circular dichroism (XRMR, XMCD) at the Pt and Au L3 edges, and ferromagnetic resonance (FMR) methods were used. With increasing thickness of a Cu or Au SL directly between the FM and the Pt layer, the Pt PIM and the damping both fall rapidly, with a relationship between damping and PIM that depends on the SL material. The PIM observed in the Au layer showed a complex dependence on the layer thickness, suggesting some hybridisation with the Pt. The role of the number and location of interfaces on the damping was demonstrated with the addition of a SL within the Pt layer, which showed that the specific details of the NM/HM interface also affects the damping. The insertion of a Cu SL within the Pt showed a measurable increase in the overall enhancement of the damping while the insertion of a Au SL into Pt had almost no effect on the damping. Together these results demonstrate the role of both PIM and of additional interfaces in the enhancement of damping in FM/HM systems, which is not fully accounted for by existing theory.