Surface silty sand soils, as a typical category of weak geotechnical materials, present major challenges in road engineering and environmental management due to their low shear strength, high susceptibility to erosion, and strong potential for dust release. This study aimed to evaluate the effect of styrene–acrylic copolymer on improving the physical and mechanical properties of these soils. Soil samples were prepared with three additive levels (2.5, 5, and 7.5% by dry weight). Standard Proctor compaction, Atterberg limits, and linear shrinkage tests were performed, followed by unconfined compressive strength (UCS) and California bearing ratio (CBR) tests after 7- and 21-day curing periods. Polymer addition slightly reduced maximum dry density from 1.79 g/cm³ (control) to 1.72–1.77 g/cm³, while optimum moisture content increased from 8% to 8.5–9.6%. The liquid limit increased from 20% to 21–23% and the plastic limit from 12% to 13–14%, with a nearly constant plasticity index (8–9%). After 21 days, UCS values reached 1.18, 1.64, and 2.03 MPa for soils with 2.5, 5, and 7.5% polymer, respectively, compared to 0.79 MPa for the untreated soil. Similarly, CBR values rose from 7.8% (control) to 11.2%, 15%, and 18.5%. Based on these results, the 7.5% dosage after 21 days is recommended as the optimum treatment, providing significant improvements in strength and bearing capacity, while simultaneously mitigating road dust emissions. Overall, the findings demonstrate the potential of styrene–acrylic polymer as an effective and sustainable solution for stabilizing weak silty sand soils.