What two forces are in balance inside the Sun?
This is an example of hydrostatic equilibrium, a balance between pressure and gravity.
Anything that's sufficiently massive will yield under the stresses internally generated by pressure and gravity. Then in effect it flows into a rounded shape that's identified as a "hydrostatic equilibrium shape". See https://en.wikipedia.org/wiki/Hydrostatic_equilibrium.
In addition to the Sun, hydrostatically equilibrated objects in our Solar System include the planets, dwarf planets like Ceres and Pluto, and relatively large moons such as our own.
Essentially the inward force of gravity is equal to the outward force of pressure created by fusion. When all the lighter elements have been used up (the hydrogen and helium mostly) the fusion of heavier elements will create more pressure than the force of gravity and then the sun will go nova.