why does a person leans in opposite direction on holding a heavy load in other hand

So that the position of centre of gravity (or center of mass) does not change.

For a system to remain in rotational equilibrium, its important that the Centre of Gravity remains inside the body, more specifically, inside the extreme point where normal force is acting. This happens so that the torque due to two opposite sense producing forces counter each other's rotational effect. In case of a person with a heavy load, the centre of gravity goes outside the person's body, to counter which the person not only leans the body to the opposite side, but also sometimes raises the other hand, so that the combined Centre of gravity of the MAN+LOAD system, remains well inside person's body. Sme is the reason for a person carrying load on his back bending in forward direction. Though it occurs to a person naturally without having knowledge of Physics, still you can try this phenomena, without bending or leaning, Since experiments are better to learn concepts than reading alone.

Thanks