In the present study, three different newly developed copolymers of poly(3-hydroxybutyrate-co-3-hydroxyvalerate) (PHBV) with 20, 40, and 60 mol % contents in 3-hydroxyvalerate (3HV) were produced by the biotechnological process of mixed microbial cultures (MMCs) using cheese whey (CW), a by-product from the dairy industry, as feedstock. The CW-derived PHBV copolyesters were first purified and then processed by solution electrospinning, yielding fibers of approximately 2 μm in cross-section in all cases. The resultant electrospun PHBV mats were, thereafter, post-processed by annealing at different temperatures, below their maximum of melting, selected according to their 3HV content in order to obtain continuous films based on coalesced fibers, so-called biopapers. The resultant PHBV films were characterized in terms of their morphology, crystallinity, and mechanical and barrier properties to assess their potential application in food packaging. The CW-derived PHBV biopapers showed high contact transparency but a slightly yellow color. The fibers of the 20 mol % 3HV copolymer were seen to contain mostly poly(3-hydroxybutyrate) (PHB) crystals, the fibers of the 40 mol % 3HV copolymer a mixture of PHB and poly(3-hydroxyvalerate) (PHV) crystals and lowest crystallinity, and the fibers of the 60 mol % 3HV sample were mostly made of PHV crystals. To understand the interfiber coalesce process undergone by the materials during annealing, the crystalline morphology was also assessed by variable-temperature both combined small-angle and wide-angle X-ray scattering synchrotron and Fourier transform infrared experiments. From these experiments and, different from previously reported biopapers with lower 3HV contents, all samples were inferred to have a surface energy reduction mechanism for interfiber coalescence during annealing, which is thought to be activated by a temperature-induced decrease in molecular order. Due to their reduced crystallinity and molecular order, the CW-derived PHBV biopapers, especially the 40 mol % 3HV sample, were found to be more ductile and tougher. In terms of barrier properties, the three copolymers performed similarly to water and limonene, but to oxygen, the 40 mol % sample showed the highest relative permeability. Overall, the materials developed, which are compatible with the Circular Bioeconomy organic recycling strategy, can have an excellent potential as barrier interlayers or coatings of application interest in food packaging.