A charged capacitor will have the same mass as an uncharged one, because charge is merely an expression of the dearth of electrons at one plate and an equal surfeit at the other.

Electrons do have mass and therefore weight. PWSLACK is correct, a charged capacitor will have the same weight as an uncharged capacitor because it contains the same number of electrons. You can discharge a capacitor by connecting the leads together (see * below)to allow the excess electrons on one plate to move to the other. This gives the capacitor a 0V charge and it still contains the same number of electrons it did when it was fully charged so the mass does not change - just the potential energy level.

* Use a current limiting resistor between the leads whenever discharging a capacitor as described.

In a lead acid battery the SG rises as the battery is charged, therefore electricity must have weight.

I have an old GPS using 4 batteries. I charged 4 x 2700 ones but could not slide them into the length wise battery holder. (OK they were still warmish)

A charged capacitor or battery will have a greater mass than an uncharged one, but don't try weighing them. The increase is so very small, you'd never know it. It's the energy that adds mass.