Stardust grains that originated in ancient stars and supernovae are recovered from meteorites and carry the detailed composition of their astronomical sites of origin. We present evidence that the majority of large (μm-sized) meteoritic silicon carbide (SiC) grains formed in C-rich asymptotic giant branch (AGB) stars that were more metal-rich than the Sun. In the framework of the slow neutron captures (the s process) that occur in AGB stars, the lower-than-solar 88Sr/86Sr isotopic ratios measured in the large SiC grains can only be accompanied by Ce/Y elemental ratios that are also lower than solar and predominately observed in metal-rich barium stars - the binary companions of AGB stars. Such an origin suggests that these large grains represent the material from high-metallicity AGB stars needed to explain the s-process nucleosynthesis variations observed in bulk meteorites. In the outflows of metal-rich, C-rich AGB stars, SiC grains are predicted to be small (≃0.2 μm); large (≃μm-sized) SiC grains can grow if the number of dust seeds is 2-3 orders of magnitude lower than the standard value of 10-13 times the number of H atoms. We therefore predict that with increasing metallicity, the number of dust seeds might decrease, resulting in the production of larger SiC grains.