We study the magnetic skyrmion formation in thin-film stacks, consist of two magnetic layers separated by a non-magnetic spacer. The Landau-Lifshitz-Gilbert equation, comprising the spin precession term and the damping term with all relevant contributions, is numerically solved within the micromagnetic framework. Through extensive systematic calculations, we find that skyrmion size can be controlled by the interlayer exchange coupling, as well as the external magnetic field. z-component of the magnetization of the layers, which can be tailored by the coupling, strongly affects the skyrmion diameter. The skyrmion phase coexists with the helical phase for both types of coupling, being antiferromagnetic or ferromagnetic, in the absence of the magnetic field. The size of the skyrmions at zero field can also be controlled by the interaction. We anticipate that our predictions not only expand our fundamental understanding of the physical mechanisms responsible for skyrmion formation but also provide rational basis for the next-generation logic/memory device applications.