The early stages of aggregation kinetics in a binary mixture of asymmetric colloids, aggregating irreversibly via biotin-streptavidin bonds, are experimentally and numerically studied. Experiments are performed by DLS methods, and data are analyzed in terms of a Smoluchowski-like coagulation equation. Focus is on the case of small (S) biotin-covered particles interacting with large (L) streptavidin-covered ones. The small particles act as linkers between the large ones. The dependence of S-L and L-L aggregation rate constants on the ratio between concentration of small and large particles is investigated, to detect the concentration at which aggregation of large particles is most effective.