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The goal of this paper is to define a certain Chow weight structure for thecategory of Voevodsky's motivic complexes with integral coefficients (asdescribed by Cisinski and Deglise) over any excellent finite-dimensionalseparated scheme $S$. Our results are parallel to (though substantially weakerthan) the corresponding 'rational coefficient' statements proved by D. Hebertand the author.  As an immediate consequence of the existence of 'weights', we obtain certain(Chow)-weight spectral sequences and filtrations for any (co)homology of$S$-motives.

On weights for relative motives with integral coefficients