Two charged plates that are insulated from each other describes in electronic parts what is called a capacitor. Most electrical devices have them in one form or another.
All of electricity is based upon the electron shells of the atoms. Quantum levels of energy are transferred from one atom to the next to create a balanced system of energy potentials.
If you were to charge each plate up to 500,000 volts and separate them just far enough that a spark would not fly off one plate to transfer charge to the other plate. The charge is based upon excess (negative) or deficient (positive) ionized atoms.
The relative gravity only changes by the amount of gravity associated with the mass of the electrons and it is equivalent to moving some marbles in to equal size containers from one container to the other. Gravity is mostly omni-directional. So what you see in transferring marbles from one container to the other, is pretty much what happens to gravity when charge transfers from one plate to the other.
For the most part, gravitational influences are unchanged when considering the system of the two plates.
However, in really small amounts, the movement of the electrons can interact gravitationally with the surrounding materials. Very tiny gravitational influences too small to detect will influence the plates and shift the gravitational center of the two plates. But there is no practical use for something you can not detect, unless it is used in conjunction with other systems like an interferrometer to create some form of extremely sensitive sensor. But the electrostatic forces are far stronger than the gravitational forces, so isolating the electrostatic forces from interferring with the detection of gravitational forces would be difficult.