Frictional Force greater than Weight for FALLING OBJECT?

When the weight is small, the friction always equals to it. So it will remain stationary. That kind of friction is called static friction. It increases with the weight.

However, friction cannot increases without limit, when the static friction reaches its limit, which is determined by the nature of the surface between the falling object and the material in contact. When the static friction reaches its maximum, it will turn to be constant. So that any further increase in weight will cause increasing net force (weight - friction), resulting in a downward acceleration. That friction arises while the object is moving is called kinetic friction. In general, the constant kinetic friction is slightly less than the maximum static friction.

As explained above, the friction is always less than or equal to the weight. So it is impossible to have friction greater than the weight.

I presume that you are asking for the frictional force (or more often called the resistance force) experienced by an object falling in a fluid, such as air, not that of solid friction.

The resistance force experienced by a falling object in air, say, is proportional to the speed when the speed is low, i.e. Ff = kv
where Ff is the frictional force, v is the velocity of the object and k is a constant.

The equation describing the motion of the object is:
mg - kv =ma
where m is the mass of the object, g is the acceleration due to gravity, a is the acceleration of the object

when v is low, mg > kv and the difference (mg-kv) is positive, thus a is positive, the object is accelerating downward

As v increases, the difference (mg-kv) becomes smaller and smaller until mg=kv, then the acceleration a is zero, i.e. the object begins to move at constant speed.
Under such situation, v will not increase any further as the acceleration a is zero. In other words, the term kv will never exceed mg.

In the unrealistic situation that the resistance force kv is greater than the weight mg, the difference (mg-kv) is negative, i.e. acceleration a now becomes negative, the object is deccelerating.

Hence, this situation is physically impossible, as you can never observe an object to fall down in the air in such a way that its speed first increase and then decrease .

It is not possible.

Frictional force is a force created only for OPPOSING the force that is acting on the object. Thus the frictional force can never surpass the force, i.e. weight.

When frictional force = weight, it is said that the object has reached its terminal velocity.