Current constraints on dark matter density profiles from weak lensing are typically limited to radial scales greater than 50-100 kpc. In this paper, we explore the possibility of probing the very inner regions of galaxy/halo density profiles by measuring stacked weak lensing on scales of only a few tens of kpc. Our forecasts focus on scales smaller than the 'equality radius' (R-eq), where the stellar component and the dark matter component contribute equally to the lensing signal. We compute the evolution of R-eq as a function of lens stellar mass and redshift and show that R-eq = 7-34 kpc for galaxies with M-* = 10(9.5)-10(11.5) M-circle dot. Unbiased shear measurements will be challenging on these scales. We introduce a simple metric to quantify how many source galaxies overlap with their neighbours and for which shear measurements will be challenging. Rejecting source galaxies with close-by companions results in an similar to 20 per cent decrease in the overall source density. Despite this decrease, we show that Euclid and Wide Field Infrared Survey Telescope will be able to constrain galaxy/halo density profiles at R-eq with S/N > 20 for M-* > 10(10) M-circle dot. Weak lensing measurements at R-eq, in combination with stellar kinematics on smaller scales, will be a powerful means by which to constrain both the inner slope of the dark matter density profile as well as the mass and redshift dependence of the stellar initial mass function.