© 2021 The Author(s)Pion and kaon structural properties provide insights into the emergence of mass within the Standard Model and attendant modulations by the Higgs boson. Novel expressions of these effects, in impact parameter space and in mass and pressure profiles, are exposed via ? and K generalised parton distributions, built using the overlap representation from light-front wave functions constrained by one-dimensional valence distribution functions that describe available data. Notably, e.g. K pressure profiles are spatially more compact than ? profiles and both achieve near-core pressures of similar magnitude to that found in neutron stars.