Light and neutron scattering measurements on highly charged polyelectrolyte solutions have recently provided firm evidence for the existence of "domain structures" containing many chains, even at rather low-polymer concentrations. In the present paper, we systematically investigate the influence of counterion charge valency Z(c) on the scattering properties of sulfonated polystyrene (PSS) solutions in water with monovalent and divalent counterions. This study is part of a larger effort to identify essential factors governing polyelectrolyte domain formation and the geometric properties of these transient structures. Neutron scattering measurements indicate that the interchain correlation length xi (d) within the domains becomes larger by a factor of 1.5-2 for divalent relative to monovalent counterions. This observation is consistent with the Manning model estimate of the change in effective polymer charge density Gamma* with Z(c) and with previous observations linking xi (d) [from the peak position in the scattering intensity [I(q)] with the bare polymer charge density, Gamma. Light scattering measurements of the radius of gyration R-g,R-d of the domains indicate that their size becomes smaller for divalent counterions and with a reduction of Gamma. We observe that the "fractal" dimension of the domains measured from the low-angle scaling of I(q) depends on the chemical structure of the polyelectrolyte. Zero average contrast (ZAC) neutron scattering measurements show that the radius of gyration R-g,R-c of individual polyelectrolyte chains is also reduced for divalent counterions, suggesting that chain rigidity is strongly influenced by Gamma*. Charge valency effects on relaxation times are investigated by dynamic light scattering. As usual, two diffusive modes are observed in the light intensity autocorrelation function, G(tau). The "fast" mode becomes slower and the "slow" mode becomes faster for the divalent counterion (Mg2+), relative to the monovalent counterion (Na+). Counterion valence has a large influence on the structure and dynamics of highly charged polyelectrolyte solutions through its influence on Gamma*.