Long-lasting, high-strength plugging materials are required for deep profile control in low-permeability fractured reservoirs. In this study, a series of hyperbranched copolymer hydrogels was prepared through an aza-Michael addition-amidation-one-pot end-group coupling strategy. Linear alkylamines were used as cores to synthesize amino-terminated generation 1.0 G broom-shaped hyperbranched macromolecular backbones via a divergent route. The resulting backbones were subsequently crosslinked with linear α,ω-diepoxy-terminated poly(ethylene glycol), affording three structurally well-defined hydrogels, denoted as C2HG, C6HG, and C8HG. Structural and physicochemical characterization showed that all hydrogels possessed interconnected three-dimensional porous networks, good thermal stability, and a lower critical solution temperature of approximately 37 °C. Rheological analysis demonstrated predominantly elastic behavior, with the storage modulus (G′) consistently exceeding the loss modulus (G″), together with pronounced shear-thinning characteristics favorable for injection into deep, low-permeability formations. By varying the alkyl-chain length of the hyperbranched backbone, the balance between environmental tolerance and plugging performance could be effectively regulated. These findings establish a structure–property relationship between backbone hydrophobicity and hydrogel performance and demonstrate that PEG-crosslinked hyperbranched copolymer hydrogels are promising candidates for deep-profile control and water shutoff in high-salinity, low-permeability fractured reservoirs.