The scale invariant theory is preserving the fundamental physical properties of General Relativity, while enlarging the group of invariances subtending gravitation theory (Dirac 1973; Canuto et al. 1977). The scale-invariant vacuum (SIV) theory assumes as gauging condition that ‘The macroscopic empty space is scale invariant, homogeneous, and isotropic’. Some basic properties in Weyl’s Integrable Geometry and cotensor calculus are examined in relation with scalar–tensor theories. Possible scale invariant effects are strongly reduced by matter density, both at the cosmological and local levels. The weak field limit of SIV tends to MOND when the scale factor is taken as constant, an approximation valid (<1 per cent) over the last 400 Myr. A better understanding of the a0-parameter is obtained: it corresponds to the equilibrium point of the Newtonian and SIV dynamical acceleration. Parameter a0 is not a universal constant, it depends on the density and age of the Universe. As MOND is doing, SIV theory avoids the call to dark matter, moreover the cosmological models predict accelerated expansion.