We develop the theory of weakly S-square-difference factor absorbing ideals (weakly S-sdf ideals) in a commutative ring R, extending the notion of weakly sdf-absorbing ideals to a relative setting determined by a multiplicatively closed subset \(S\subseteq R\) . We establish their basic properties, relate them to weakly S-prime, S-sdf-absorbing, and S-semiprime ideals, and use the S-characteristic and S-invertible elements to identify conditions under which weakly S-sdf ideals strengthen to weakly S-prime or S-sdf-absorbing ideals. We further examine their behavior under homomorphic images, direct products, quotients, trivial ring extensions, amalgamated duplications, and amalgamated algebras. A complete characterization of weakly S-sdf ideals in pullback rings \(A\times _{C}B\) is obtained, showing that the property transfers precisely through the coordinate ideals together with a natural square-difference compatibility condition.
