When an object comes in contact with a rough surface and experiences an increase in friction, its weight, which is the force due to gravity, remains the same. The weight of an object is determined by its mass and the acceleration due to gravity. The force of gravity acts vertically downward, and it is independent of the surface on which the object rests.
Friction, on the other hand, is a separate force that opposes the motion or potential motion between two surfaces in contact. It arises due to the roughness or irregularities of the surfaces. Friction acts parallel to the surface and opposes the relative motion between the object and the surface it is in contact with.
While the frictional force can affect the motion of an object, it does not change the object's weight. The weight remains constant unless there is a change in the mass of the object or the acceleration due to gravity. Therefore, when an object comes in contact with a rough surface and experiences an increase in friction, its weight does not change.