Solid-state nanopores are emerging as a valuable tool for the detection and characterization of individual biomolecules. Central to their success is the realization of fabrication strategies that are both rapid and flexible in their ability to achieve diverse device dimensions. In this paper, we demonstrate the membrane thickness dependence of solid-state nanopore formation with a focused helium ion beam. We vary membrane thickness in situ and show that the rate of pore expansion follows a reproducible trend under all investigated membrane conditions. We show that this trend shifts to lower ion dose for thin membranes in a manner that can be described quantitatively, allowing devices of arbitrary dimension to be realized. Finally, we demonstrate that thin, small-diameter nanopores formed with our approach can be utilized for high signal-to-noise ratio resistive pulse sensing of DNA.