Using in situ magneto-optical Kerr effect measurements and phenomenological modeling, we study the tunability in both the magnetization anisotropy and magnetic coupling of Fe nanodots on a curved Cu(111) substrate with varying vicinity. We observe that, as the terrace width w decreases, the magnetization anisotropy increases monotonically, faster when w is smaller than the nanodot size d. In contrast, the magnetic coupling strength also increases until w approximately d, after which it decreases steeply. These striking observations can be rationalized by invoking the counterintuitive dimensionality variation of the surface electrons mediating the interdot coupling: the electrons are confined to be one dimensional (1D) when w > or = d, but become quasi-2D when w < d due to enhanced electron spillover across the steps bridged by the nanodots.