Lipopolymers are known to form a two-dimensional physical network (physical gel) at the air-water interface that is stabilized by two different types of associative interactions: microcondensation of alkyl chains of lipopolymers to form small clusters and physical junction zones linking neighboring polymer chains stabilized by hydrogen bonding of water molecules. In this study we present surface rheology and film balance experiments on amphiphilic PEG lipopolymers of different molecular weights of their polymer moiety (MW: 750, 1000, 2000, 3000, 5000) at the air-water interface. Our experimental data show that the gelation transition shifts within the TAW range of 1000-5000 to smaller areas per molecule as the polymer chain length gets shorter until it reaches a specific minimum area where no further change is observed (MW = 1000). Surface rheology data of the storage modulus indicate a qualitative difference between higher MW species (MW: 2000, 3000, 5000) and lower MW species (MW: 750, 1000). While the well-known power law dependence above the gelation point can be observed in the first case, a breakdown of the network after an initial power law-like behavior is found in the latter one. Our data suggest that a sufficient area mismatch between polymer and lipid moieties of these peculiar amphiphiles is essential for a stable two-dimensional physical network to form.