Magmatic density and viscosity exert fundamental controls on the eruptibility of magmas. In this study, we investigate the extent to which magmatic physical properties control the eruptibility of magmas from Iceland's Northern Volcanic Zone (NVZ). By studying subaerial flows of known age and volume, we are able to directly relate erupted volumes to magmatic physical properties, a task that has been near-impossible when dealing with submarine samples dredged from mid-ocean ridges. We find a strong correlation between magmatic density and observed erupted volumes on the NVZ. Over 85\% of the total volume of erupted material lies close to a density and viscosity minimum that corresponds to the composition of basalts at the arrival of plagioclase on the liquidus. These magmas are buoyant with respect to the Icelandic upper crust. However, a number of small-volume eruptions with densities greater than typical Icelandic upper crust are also found in Iceland's neovolcanic zones. We use a simple numerical model to demonstrate that the eruption of magmas with higher densities and viscosities is facilitated by the generation of overpressure in magma chambers in the lower crust and uppermost mantle. This conclusion is in agreement with petrological constraints on the depths of crystallisation under Iceland.