Ring-opening alternating copolymerization (ROAC) of cyclic anhydrides and epoxides has emerged as a powerful strategy to produce degradable polyesters with a diverse array of structures from the combination of two distinct building blocks. In this work, we exploited the organocatalytic ROAC of cyclic anhydrides and a functional epoxide, t-butyl glycidoxy acetate, followed by acidic deprotection to access degradable polyesters with carboxylic acid pendants. To study the interplay between monomers, diglycolic anhydride and glutaric anhydride were used as cyclic anhydrides to prepare two polyesters. In particular, the effects of the oxygen heteroatom in the cyclic anhydrides on the properties of the carboxylic acid-containing polyesters were investigated. The introduction of the oxygen heteroatom into the cyclic anhydrides significantly influenced their thermal properties and pH-dependent self-association behavior in an aqueous solution. Furthermore, molecular dynamics simulations elucidate that the number and type of hydrogen bonds play a crucial role in the self-association behavior between the polymers both in the solution and bulk states. The findings of this study highlight the importance of the interplay between monomers in the design of functional polyesters with tunable properties.