Epitaxial thin-film heterostructures offer a versatile platform for realizing topological surface states (TSSs) that may be emergent and/or tunable by tailoring the atomic layering in the heterostructures. Here, as an experimental demonstration, Sb and Bi2Te3 thin films with closely matched inplane lattice constants are chosen to form two complementary heterostructures: Sb overlayers on Bi2Te3 (Sb/Bi2Te3) and Bi2Te3 overlayers on Sb (Bi2Te3/Sb), with the overlayer thickness as a tuning parameter. In the bulk form, Sb (a semimetal) and Bi2Te3 (an insulator) both host TSSs with the same topological order but substantially different decay lengths and dispersions, whereas ultrathin Sb and Bi2Te3 films by themselves are fully gapped trivial insulators. Angle-resolved photoemission band mappings, aided by theoretical calculations, confirm the formation of emergent TSSs in both heterostructures. The energy position of the topological Dirac point varies as a function of overlayer thickness, but the variation is non-monotonic, indicating nontrivial effects in the formation of topological heterostructure systems. The results illustrate the rich physics of engineered composite topological systems that may be exploited for nanoscale spintronics applications.