We revisit collisionless major and minor mergers of spheroidal galaxies in the context of recent observational insights on compact massive early-type galaxies at high redshift and their rapid evolution on cosmological time-scales. The simulations are performed as a series of mergers with mass ratios of 1:1 and 1:10 for models representing pure bulges as well as bulges embedded in dark matter haloes. For major and minor mergers, respectively, we identify and analyse two different processes, violent relaxation and stripping, leading to size evolution and a change of the dark matter fraction within the observable effective radius re. Violent relaxation – which is the dominant mixing process for major mergers but less important for minor mergers – scatters relatively more dark matter particles than bulge particles to radii r < re. Stripping in minor mergers assembles stellar satellite particles at large radii in halo-dominated regions of the massive host. This strongly increases the size of the bulge into regions with higher dark matter fractions leaving the inner host structure almost unchanged. A factor of 2 mass increase by minor mergers increases the dark matter fraction within the effective radius by 80 per cent whereas relaxation in one equal-mass merger only leads to an increase of 25 per cent. We present analytic corrections to simple one-component virial estimates for the evolution of the gravitational radii. These estimates are shown to underpredict the evolution of the effective radii for parabolic minor mergers of bulges embedded in massive dark matter haloes. If such a two-component system grows by minor mergers alone its size growth, re ∝ Mα, reaches values of α ≈ 2.4, significantly exceeding the simple theoretical limit of α = 2. For major mergers the sizes grow with α ≲ 1. In addition, we discuss the velocity dispersion evolution and velocity anisotropy profiles. Our results indicate that minor mergers of galaxies embedded in massive dark matter haloes provide a potential mechanism for explaining the rapid size growth and the build-up of massive elliptical systems predicting significant dark matter fractions and radially biased velocity dispersions at large radii.