The amount of the gravitational force doubles.
This is because the gravitational force between two objects is proportional to the product of their masses. According to Newton's law of universal gravitation, \( F = G \frac{m_1 m_2}{r^2} \). If the mass of one object (let's say \( m_1 \)) doubles, the gravitational force \( F \) will also double, assuming the mass of the other object (\( m_2 \)) and the distance (\( r \)) remain constant.