In this work, we report on the synthesis of a series of polyesters based on 1,6-hexanediol, sebacic acid, and N,N’-dimethylene-bis(pyrrolidone-4-carboxylic acid) (BP-C2), of which the latter is derived from renewable itaconic acid and 1,2-ethanediamine. Copolymers with a varying amount of BP-C2 as dicarboxylic acid are synthesized using a melt-polycondensation reaction with the aim of controlling the hydrolysis rate of the polymers in water or under bioactive conditions. We demonstrate that the introduction of BP-C2 in the polymer backbone does not limit the molecular weight build-up, as polymers with a weight average molecular weight close to 20 kg/mol and higher are obtained. Additionally, as the BP-C2 moiety is excluded from the crystal structure of poly(hexamethylene sebacate), the increase in BP-C2 concentration effectively results in a suppression in both melting temperature and crystallinity of the polymers. Overall, we demonstrate that the BP-C2 moiety enhances the polymer’s affinity to water, effectively improving the water uptake and rate of hydrolysis, both in demineralized water and in the presence of a protease from Bacillus licheniformis.