The conformation of a weakly dissociating (annealing) polyelectrolyte chain end-tethered to a similarly or oppositely charged planar surface is analyzed in the framework of scaling arguments. For a similarly charged interface an analytical model is also utilized. We demonstrate that at low salt concentration in bulk solution there is a strong coupling between the polyelectrolyte conformation and its degree of ionization. In the case of an oppositely charged (adsorbing) surface, adsorption promotes ionization of the annealing polyelectrolyte. As a result, the adsorbed layer thickness decreases as a function of surface charge density more rapidly for an annealing polyelectrolyte than for a quenched one. In the case of a similarly charged (repulsive) surface the chain ionization is suppressed, and the annealing polyelectrolyte chain is less extended than the quenched one. Moreover, an increase in surface charge density leads to non-monotonous extension of the tethered polyelectrolyte.