solar system - Why is the Sun's density less than the inner planets?

All the other answers address the density of the sun, but I feel that none of them actually addresses the OP's misconception. OP seems to think denser material should sink, but this is not the case. Thus Pluto is denser than Uranus, but orbits further out. There is nothing strange about this.

The reason is that orbital energy is conserved indefinitely unless there is some kind of interaction. A planet feels "weightless" just like an astronaut in a space station, because it is in freefall towards the centre of mass of the solar system. Unless it interacts with another body, matter, regardless of its density, will continue to orbit at the same distance from the centre of mass of the solar system, as a consequence of conservation of energy.

Density only becomes an issue when objects come into physical contact, and a body receives a push from another body.

Thus in an orbiting spacecraft, dense objects just float around "weightlessly" and do not "fall" to the "bottom." Both the air and the objects in the spaceship are experiencing gravity, but they are falling at the same rate, so they do not push each other.

When the spacecraft is on the ground, the Earth's surface pushes up on the spacecraft, and prevents it from accelerating towards the centre of the earth. Under these circumstances, the denser objects, if unconstrained, will fall towards the floor of the spacecraft, displacing the less dense air. When they hit the floor, they receive a push from it, preventing their continued fall.

In space objects do not push each other by physical contact, so density makes no difference. A trillion tons of iron and a trillion tons of silica may have different volumes, but they have the same mass, therefore so long as their interactions with the rest of the solar system are purely gravitational, both will behave identically.

On the other hand, matter that has coalesced into a planet, sun, or moon will become stratified by density. In the case of a moon or rocky planet this is almost entirely due to the denser materials sinking and forcing the more voluminous ones to rise. In the case of the sun or a gas giant the core will also be denser due to compression. In addition to contact forces, friction is also present. Note also that friction is necessary for orbital decay: without it satellites will orbit at the same height indefinitely.