An eco-friendly $\text{poly}\left(\mathrm{\epsilon }-\text{caprolactone}\right)\left(\mathrm{PCL}\right)$ based asymmetric membrane was prepared using N-methyl-2-pyrrolidone (NMP) as a solvent and poly(ethylene glycol) (PEG) pore former in a water medium by the nonsolvent-induced phase separation method (NIPS). The current study investigates the effect of pore-forming, hydrophilic agent PEG with molecular weights ranging from low to high in two different dope compositions of 10% and 12%. Structural and morphological features of the membranes were studied and confirmed asymmetric nature and finger-like morphology. Porosity and pore size significantly reduced when the dope composition increased. Whereas increased porosity with a slight reduction in the pore size was observed with the increase in the additive molecular weight. The filtration performance, porosity, and hydrophilic properties were analyzed. The water contact angle of the membranes decreases from 69.2 to 56.2 in 10% dope and 73.9 to 59.1 in 12% dope composition. The pure water flux also increased from 68.23 to 153 $\mathrm{L}{\mathrm{m}}^{-2}{\mathrm{h}}^{-1}$ as the additive molecular weight increased. Rejection studies were conducted with an oil and immunoglobulin protein as permeate and the membrane incorporating the highest molecular weight PEG showed 98% rejection for protein and 89% rejection for oil with a flux recovery ratio of 87.5%.