There is no high pressure at the center of Uranus or any planet. Materials at the center are surrounded by an essentially uniform mass field.
ML/NJ
You are mistaken. Your symmetry argument could validly demonstrate that the local gravitational acceleration ( weight of a given mass ) decreases to zero at the center of a planet. However the pressure increases to the center of the planet.
Speaking loosely, the pressure on the volume element is independent of its own weight but rather caused by the weight (mutual attraction forces) of all the materials around it which are transmitted across it.
Citation please!