We examine the effects of horizontally layered heterogeneities on the spreading of two-phase gravity currents in a porous medium, with application to numerous environmental flows, most notably geological carbon sequestration. Heterogeneities, which are ubiquitous within geological reservoirs, affect the large-scale propagation of two-phase flows through the action of small-scale capillary forces, yet the relationship between these small- and large-scale processes is poorly understood. Here, we derive a simple upscaled model for a gravity current under an impermeable cap rock, which we use to investigate the effect of a wide range of centimetre-scale heterogeneities on kilometre-scale plume migration. By parameterising in terms of different types of archetypal layering, we assess the sensitivity of the gravity current to the distribution and magnitude of these heterogeneities. Furthermore, since field measurements of heterogeneities are often sparse or incomplete, we quantify how uncertainty in such measurements manifests as uncertainty in the macroscale flow predictions. Using realistic parameter values, we demonstrate that heterogeneities can enhance plume migration speeds by as much as 200 %, and that uncertainty in field measurements can have dramatic consequences on flow predictions, particularly in post-injection scenarios where the role of capillary forces in heterogeneities is accentuated.