A first attempt at a semiquantitative study of molecular weight (MW) and molecular weight distribution (MWD) in cooked grape must and traditional balsamic vinegar (TBV) with increasing well-defined age was performed by high-performance liquid size exclusion chromatography (SEC) using dual detection, that is, differential refractive index (DRI) and absorbance (UV-vis) based detectors. With this aim, MW and MWD, including number- and weight-average MW and polydispersity, were determined with respect to a secondary standard and then analyzed. All investigated vinegar samples were recognized as compositionally and structurally heterogeneous blends of copolymers (melanoidins) spreading over a wide range of molecular sizes: the relative MW ranged from 2 to >2000 kDa. The extent of the polymerization reactions was in agreement with the TBV browning kinetics. MWD parameters varied asymptotically toward either upper or lower limits during aging, reflecting a nonequilibrium status of the balance between polymerization and depolymerization reactions in TBV. MWD parameters were proposed as potential aging markers of TBV.