Weak lensing alters the size of images with a similar magnitude to the distortion due to shear. Galaxy size probes the convergence field and shapes the shear field, both of which contain cosmological information. We show the gains expected in the dark energy figure of merit if galaxy size information is used in combination with galaxy shape. In any normal analysis of cosmic shear, galaxy sizes are also studied, so this is extra statistical information that comes for free and is currently unused. There are two main results in this Letter: first, we show that size measurement can be made uncorrelated with ellipticity measurement, thus allowing the full statistical gain from the combination, provided that √area is used as a size indicator; secondly, as a proof of concept, we show that when the relevant modes are noise dominated, as is the norm for lensing surveys, the gains are substantial, with improvements of about 68 per cent in the figure of merit expected when systematic errors are ignored. An approximate treatment of such systematics such as intrinsic alignments and size–magnitude correlations, respectively, suggests that a much better improvement in the dark energy figure of merit of even a factor of ∼4 may be achieved.