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Understanding what happens when tunneling inside a star requires knowledge of a concept known as a 'uniform-density star.' The term refers to a celestial body with density that is constant throughout its volume. Imagine a gigantic sphere of material where each slice, from core to surface, has the same mass per unit volume. This uniformity has surprising implications for gravity within the star.

When you're outside such a star, you can treat it, thanks to its symmetry, as if all its mass were concentrated at the center. However, once you start to move inward, the scenario changes. Each shell of material you pass no longer influences you gravitationally, leading to a decrease in the gravitational force as you get closer to the center. As a result, your weight, which is the force exerted on you by gravity, would also decrease.

A pivotal part of understanding gravity in and around spherical objects is the Shell Theorem. This principle, which arose from the work of Sir Isaac Newton, tells us that a shell of uniform thickness and density exerts no net gravitational force on an object inside it. In other words, the gravitational forces exerted by the different parts of the shell cancel each other out. Conversely, if you are outside the shell, it can be treated as if all its mass were concentrated at its center.

The Shell Theorem is essential in explaining why your weight would decrease if you tunnel inside a uniform-density star: the layers, or 'shells', of star material above you have no effect on your gravitational pull, thus only the mass inward from your location counts towards the force you feel.

Newton's law of universal gravitation is a fundamental principle that describes the attractive force between any two masses. According to this law, every point mass in the universe is attracted to every other point mass with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers. The law is mathematically expressed as \( F = G \frac{m_1 m_2}{r^2} \), where \( F \) is the gravitational force, \( G \) is the gravitational constant, \( m_1 \) and \( m_2 \) are the masses of the objects, and \( r \) is the distance between the two.

The inverse-square nature of the law means that when the distance between two objects decreases, the gravitational force increases rapidly. This property underpins why your weight would rise if you stood on the surface of a shrinking star—as the star contracts, you are closer to all of its mass, and the gravitational force on you would become stronger.

The weight variation in celestial bodies refers to how an object's weight changes depending on its location in relation to other masses, especially when considering large-scale structures like stars and planets. An object’s weight is the force with which it is pulled by another object’s gravity, which depends not only on its mass but also on the gravitational pull it experiences. Factors affecting this are the mass of the celestial body it is on or near, the distance to the body's center of mass, and the distribution of that mass.

For instance, on a uniform-density star, as you tunnel inward, your distance to the varied masses changes, and due to the Shell Theorem, your weight decreases. In contrast, as a star's size diminishes but its mass remains the same, the compactness increases the surface gravity, and thus your weight increases if you’re on its surface. These variations are quintessential examples of how gravity is not a constant experience across the universe but is instead deeply influenced by the unique geometries and masses of celestial bodies.