The case of the flat surface interface between pure liquid water and water vapor has, under the assumption of mechanical equlibrium, equal pressure across the surface. However, mechanical equilibrium in the case of the curved surface of a water droplet results in a pressure difference given by $P_w - P_v = \frac{2\sigma}{r}$, where $P_w$ is the pressure associated with the water droplet, $P_v$ is the pressure associated with the water vapor, $\sigma$ is the surface tension of the droplet measured in units of energy per area or force per unit length, and $r$ is the radius of the droplet. (See page 110 of ``Clouds and Precipitation'' by Pao K. Wang.)

The pressure differenece results, essentially, in a greater rate of evaporation $R_e$ for the curved surface relative to the flat surface. Consequently, vapor pressure must increase over the surface in order for the rate of condesation $R_c$ to match the rate of evaporation. That is, vapor pressure $e$ must be greater than $e_s$ (as determined by the flat surface case), resulting in the need for relative humidities greater than 100% for the cloud droplet to exist, especially at smaller droplet diameters as shown in the graph below.

The value of the required relative humidty to sustain the droplet as a function of droplet radius can be show to be given by $e_s(r) = e_0 \cdot e^{A/r}$, where $A$ is a value dependent temperature, the gas constant, the surface tension, and $e_0$ is the require saturation vapor pressure over a flat surface (P.K. Wang - page 119) .