The kinetics of the electrostatic layer-by-layer adsorption of a weakly charged polycation, poly(allylamine hydrochloride), PAH, and a polyanion containing an azobenzene chromophore, P-Azo, was studied using UV-vis spectroscopy and ellipsometry. The thickness of the multilayer films was first measured over the adsorption pH range of 3 to 11, and the growth of multilayers was examined as function of time and concentration. Films assembled in bath pH near that of their pK(a) value produced both the thickest films and displayed remarkably rapid adsorption isotherms. In some PAH/P-Azo films, a significantly large thickness was achieved in less than 5 s, which is more than 2 orders of magnitude faster than what is usually observed. We show that this anomalously rapid adsorption is a consequence of the weak acid-base nature of the layers. In addition, the role of counterion displacement in multilayer formation from weakly charged polyelectrolytes was explored by examining the rates of P-Azo adsorption in PAH/P-Azo multilayer formation from polymer solutions containing the counterion series F-, Cl-, Br-, and I-. Multilayers of PAH/P-Azo prepared from solutions containing I- ions exhibited 21% greater adsorption at saturation (t = 60 s) than those containing an equal concentration of F- ions. We provide a simple scaling rationalization relating the counterion binding energies with the observed rates of displacement by an adsorbing polymer segment.