The invention pertains to the technical field of precision damping, and is a heavy-load precision damper and a damping system comprising thereof. The damper comprises a low-rigidity air spring with variable damp, an inverted-pendulum structure with low horizontal rigidity and a group of three-degree-of-freedom active damping actuators. The structure of the air spring is external-internal annularity double air chambers communicated with a throttling hole; the inverted-pendulum structure comprises a main supporting rod and at least two flexible swing rods and is located in an annular air chamber; and the active damping actuator comprises three linear motors arranged in an orthogonal manner. The heavy-load precision damper vertically generates large bearing force by the air spring, respectively separates vertical and horizontal vibration transmission by the air spring and the inverted-pendulum structure, and actively controls the damp vibration by acting force of the vertical and horizontal linear motors. The damping system comprises at least three heavy-load precision dampers arranged in the shape of a polygon, and realizes six-degree-of-freedom precision damping of a vibration-isolation device by the mutual action of every heavy-load precision dampers.