The higgs field is responsible for giving mass to the gauge bosons of the weak interaction and also to the massive particles in the standard model of particle physics.
The macroscopic masses of composite particles like protons, neutrons and nuclei are mainly the result of the invariant masses of summed four vectors of the elementary particles that compose them; it is not just the sum of the masses of the particles, because special relativity reigns at that level . The higgs field contribution to the mass is small.The proton mass is about a GeV, the valence quarks add up to a few MeV. It is the sea of quark and antiquarks and gluons with their four vectors that generate the measured proton mass (attempts at modeling with lattice QCD).
It is at the classical level that masses can be summed and Archimedes principle applied. At that level the higgs field is not relevant.
At cosmological times , once quantization of gravity and a unified theory is found, it might be reasonable to expect variations in the effect of the higgs at symmetry breaking times with respect to the gravitational fields at that time, but after symmetry breaking the situation is stable, as far as lensing etc goes. It is the classical mechanics masses that apply