Motivated by the defect-mediated two-stage melting theory, extensive experiments have been concluded on free-standing films of a liquid-crystal sample which exhibits the isotropic-smectic-A-hexatic B-crystal-B bulk phase sequence. For a two-layer film, which is virtually two-dimensional, our calorimetric measurement shows an apparently divergent anomaly near the smectic-A-hexatic-B transition. Its anomaly has a dominant fluctuation contribution and can be fitted to a power law with an exponent α ≈ 0.37 ± 0.05, in disagreement with the theoretical prediction. Thicker films exhibit surface-initiated layer-by-layer (LBL) wetting transition upon cooling. Moreover, these films also exhibit interesting LBL thinning transitions above the bulk clearing temperature.