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Two-dimensional topological insulators (TIs) are distinguished by their Dirac edge states, and a topological phase transition between trivial and nontrivial states that can be tuned by composition, strain, or film thickness. In this work, we demonstrate the molecular beam epitaxial growth of Bi and Sb films on 3D TI Bi₂Te₃, and investigate their electronic properties using scanning tunneling microscopy/spectroscopy and density functional theory. We find that while Bi grows layer-by-layer, the growth mode for Sb is thickness dependent: below three bilayers (BLs) is step flow, and above layer-by-layer. This facilities a systematic study of their thickness-dependent electronic properties by scanning tunneling spectroscopy. We show that while few BL Bi films are 2D TIs, Sb film is a trivial insulator at below three BLs, which evolves into a 2D TI above three BLs, confirming earlier theoretical predictions.