Abstract: The discovery of the Higgs boson at the Large Hadron Collider has confirmed a dynamical mechanism with which the intermediate vector bosons responsible for the weak interactions acquire mass. The same mechanism also gives mass to all the elementary building blocks of matter, as confirmed by further experiments at CERN. The fact that the masses of fundamental fermions are dynamical variables depending on the Higgs field has important consequences in a gravitational setting, as masses can be modulated by changing the vacuum expectation value of the Higgs field in regions with strong space-time curvature. We will describe a variety of contexts in which 'Higgs shifts' of masses and other observables have phenomenological implications. Finally, we will discuss a conjecture according to which weak interactions could be considered as the microscopic counterpart of gravitation, or vice versa that gravity at the macroscopic scale is a residual effect of weak interactions. A simple and coherent picture seems to emerge, with implications in high precision and high energy physics, as well as in cosmology. In particular, the concept of 'unparticle' previously introduced by Howard Georgi seems to be corroborated by such a scenario, implying no further particle discoveries at energies above the Fermi scale.