We investigate the water-solubility upon salt additions, of homogeneous families of sulfobetaine-based polyzwitterions. These polymers bear both positive ammonium, and negative sulfonate charges on each monomer and as a result present an upper critical solution temperature (UCST) in the 0-100 degrees C temperature range. Two chemistries are investigated, with either a carboxylate-carrying function (SPE) or an amido-carrying one (SPP). In agreement with the literature published on pSPEs, we find that an addition of simple salts improves the water-solubility of pSPEs, as well as that of pSPPs, yet only once a threshold concentration of added salt has been reached in the solution. We verify using scaling arguments that the onset of solubility promotion, corresponds exactly to the complete screening of the attraction between positive and negative charges inside a polyzwitterionic coil. On the contrary, for salt concentrations smaller than the threshold concentration, we observe that an addition of salt can be adverse to the solubility of polyzwitterions, depending on the degree of polymerization, the type of salt, and the type of zwitterionic motive. Thanks to zeta-potential measurements and systematic variations of these three parameters, we demonstrate, in agreement with theoretical prediction, that this molecular weight-dependent enhanced solubility at small salt concentrations is due to charge asymmetry resulting from partial hydrolysis, combined with specific interactions between salts and zwitterion constituents, evidencing the complexity of the solution behavior of these macromolecules. We thereby reconcile the different behaviors in the domains of low- and high-salinity.