The different triplet sequences in high molecular weight aromatic copolyimides comprising pyromellitimide units ("I") flanked by either ether-ketone ("K") or ether-sulfone residues ("S") show different binding strengths for pyrene-based tweezer-molecules. Such molecules bind primarily to the diimide unit through complementary pi-pi-stacking and hydrogen bonding. However, as shown by the magnitudes of H-1 NMR complexation shifts and tweezer-polymer binding constants, the triplet "SIS" binds tweezer-molecules more strongly than "KIS" which in turn binds such molecules more strongly than "KIK". Computational models for tweezer-polymer binding, together with single-crystal X-ray analyses of tweezer-complexes with macrocyclic ether-imides, reveal that the variations in binding strength between the different triplet sequences arise from the different conformational preferences of aromatic rings at diarylketone and diarylsulfone linkages. These preferences determine whether or not chain-folding and secondary pi-pi-stacking occurs between the arms of the tweezer-molecule and the 4,4'-biphenylene units which flank the central diimide residue.