We study genus 2 Hilbert-Siegel varieties, i.e. Shimura varieties SK corresponding to the group GSp4,F over a totally real field F , along with the relative Chow motives λV of abelian type over SK obtained from irreducible representations Vλ of GSp4,F . We analyse the weight filtration on the degeneration of such motives at the boundary of the Baily-Borel compactification and we find a criterion on the highest weight λ , potentially generalisable to other families of Shimura varieties, which characterizes the absence of the \textit{middle weights} 0 and 1 in the corresponding degeneration. Thanks to Wildeshaus' theory, the absence of these weights allows us to construct Hecke-equivariant Chow motives over Q , whose realizations equal interior (or intersection) cohomology of SK with Vλ -coefficients. We give applications to the construction of homological motives associated to automorphic representations.