Also, the end-groups have molecular weights less than 500 Da.

As polymers are formed by the addition of repeating units, their properties can be predicted (estimated) by Group Additive methods (van Krevelen method) or group contribution method (Askadskii method). If you know the structure of the repeating unit with the functional group, then the thermodynamic parameters can be estimated by van Krevelen method.

You can try a dye that is soluble in water and do an experiment with the PEG and methylene chloride. PEG while paritioning would take the dye into the organic phase. and thereby reduce the colour intensity which may be ,easured by colorimetry or spectrophotometry.