This study examines the right barycentric shift on a probability simplex contained in a hybrid weighted sequence space. The underlying hybrid norm is obtained from the intersection of two multiplier components associated with a boundary-anchored Cesaro--difference domain. After a diagonal isometry transfers the simplex to the space of absolutely summable sequences, an adjacent-coupling term is added to the norm. The Lipschitz coefficient of every iterate is then represented by a variational formula over zero-sum coefficient vectors. For periodic coupling profiles, the formula reduces the asymptotic question to finitely many residue classes. We prove that the shift is asymptotically nonexpansive precisely when the periodic profile is identically zero. The same argument shows that an eventually periodic profile has this property precisely when the entire profile is zero: a nonzero periodic tail creates a recurrent boundary defect, whereas a nonzero initial coupling creates a persistent denominator defect after the tail has vanished. Restricting the variational problem to vectors supported on two consecutive periods gives finite-dimensional linear programs and computable certified lower bounds for the iterate defect. For a constant profile, the resulting expression agrees with the exact coefficient. These results separate the geometry of the underlying weighted space from the additional information carried by adjacent couplings.