Over-lying means to cover or place something on top of another. The antonym for over-lying is underlaying or underpinning, which means to support or provide a foundation for something. While over-lying creates an added layer on top, underlaying is the base or foundation for something. To further illustrate, if we were talking about a rug, the over-lying would be the actual rug, while the underlaying would be the padding beneath it. In other contexts, the opposite of over-lying could be removing or uncovering, but they do not fully capture the meaning of supporting or providing a foundation.