We report the synthesis and structural characterization of a 2D metal-organic framework with AB-packing layers, [Co2(pybz)2(CH3COO)2]·DMF (Co2, pybz= 4-(4-pyridyl)benzoate), containing a stable (4,4)-grid network fabricated by paddle-wheel nodes, ditopic pybz, and acetate ligands. After removal of the guest, the layer structure is retained but reorganized into an ABCD packing mode in the activated phase (Co2a). Consequently, the intralayer square windows (7.2 × 5.0 Å2) close, while the interlayer separation is decreased slightly from 3.69 to 3.45 Å, leaving a narrow gap. Importantly, the dangling methyl group of the acetate with H-bonds to the adjacent layers and also the well-distributed π-π interactions between the aromatic rings of neighboring layers facilitate the structural stability. These weak supramolecular interactions further allow for favorable dynamic exfoliation of the layers, which promotes efficient adsorption of C2H2 (41.6 cm3 g-1) over CO2 with an adsorption ratio of 6.3 (0.5 bar, 298 K). The effective separation performance of equimolar C2H2/CO2 was verified by cycling breakthrough experiments and was even tolerable to moisture (R.H = 52%). DFT calculations, in situ PXRD, and PDF characterization reveal that the favorable retention of C2H2 rather than that of CO2 is due to its H-bond formation with the paddle-wheel oxygen atoms that triggers the increase in interlayer separation during C2H2 adsorption.