We show that the atomistic structure of step edges is crucial for understanding of the interlayer mass transport in homoepitaxy. Performing atomic scale calculations for double layer Cu islands on Cu(111), we reveal that detachment energies of atoms from islands in the vicinity of the sted edges are reduced. The interplay between diffusion barriers for the mass transport and the mesoscopic strain is demonstrated. Our study presents evidence that the mesoscopic mismatch between the upper and the lower islands leads to the shape transitions at the edge and influences the interlayer mass transport.