We discuss the impact on the stau masses of additional $D$ terms in $U(1)$-extended minimal supersymmetric standard models. We show, explicitly for the B-L supersymmetric standard model, that these contributions can play a crucial role in the explanation of the enhanced diphoton decay rate of a standard-model-like Higgs particle around 125 GeV. Even in the most constrained scenario with universal scalar and gaugino masses, it is possible to obtain a sizable enhancement and, in addition, the correct relic density for the LSP. Furthermore, a lighter $CP$-even scalar that could fit the LEP excess at 98 GeV is viable.