When an electroscope is charged, its two leaves repel each other and remain at an angle. What balances the electric force of repulsion so that the leaves don't separate further?

There are two forces acting on the leaves. 1. Electrostatic force acting horizontally repelling one leaf from the other.

2. The force of gravity acting vertically downwards.

When each leaf is at 45 deg to the vertical the electrostatic force will equal the gravitational force on each leaf.