Think about just the bottom of the rope, the bit that is connected directly to the object. There is a downwards force on the object from gravity - it's ##mg##. However, the object is not accelerating so we know that the net force on it is zero. Thus, the little bit of rope attached to the object must be exerting an upwards force on the object, also of magnitude ##mg## so that the net force comes out zero.
Because that little bit of rope is exerting an upwards force of ##mg## on the object, we also know from Newton's third law that the object is exerting a downwards force ##mg## on the little bit of rope. But the little bit of rope is not accelerating, so the net force on it is zero - the next little bit of rope above it must be exerting an upwards force, and again Newton's third law says that there is an equal and opposite downwards force on that bit. Eventually we get to the top, where the ceiling exerts an upwards force sufficient to exactly cancel the downwards gravitational force on the rope and the object.
At every point along the rope, the tension is opposing the force of gravity on the object and all the rope below that point. If the mass of the object is ##m## and the mass of the entire length of rope is ##m_R##, the tension at the bottom is ##mg## (what it takes to make the net force on the object be zero) and the tension at the top is ##(m+m_R)g## (what it takes to make the net force on the object plus the rope be zero).
