We compared the total mass density profiles of three different types of galaxies using weak gravitational lensing: (i) 29 galaxies that host quasars at (z) over bar similar to 0.32 that are in a post-starburst quasar (PSQ) phase with high star formation indicating recent merger activity, (ii) 22 large elliptical galaxies from the Sloan Lens ACS Survey (SLACS) sample that do not host a quasar at (z) over bar similar to 0.23, and (iii) 17 galaxies that host moderately luminous quasars at (z) over bar similar to 0.36 powered by disc instabilities, but with no intense star formation. In an initial test we found no evidence for a connection between the merger state of a galaxy and the profile of the halo, with the PSQ profile comparable to that of the other two samples and consistent with the Leauthaud et al. study of moderately luminous quasars in Cosmic Evolution Survey (COSMOS). Given the compatibility of the two quasar samples, we combined these and found no evidence for any connection between black hole activity and the dark matter halo. All three mass profiles remained compatible with isothermality given the present data.