Calculate the weight of an object on earth surface having 600km from surface of earth?

Your question seems to contradict itself. You said "on Earth surface" and then you said "600 km from surface of the Earth" ... both in the same sentence.

I'll assume that the object is actually 600 km from surface of the Earth, because that makes the question (and the answer) more interesting.

We know that the weight of any object is (mass) x (gravity). Those are the two numbers we need in order to calculate the object's weight. Mysteriously, you haven't told us either one.  We'll call the object's mass ' M ' (clever, eh ?), and we'll calculate the value of gravity up there where the object is located.

We now that the acceleration of gravity is inversely proportional to the square of the distance between the centers of two objects.  When an object is on the Earth's surface, it's 6,371 km from Earth's center, and the acceleration of gravity there is 9.8 m/s².  

The object in the question is 600 km farther from Earth's center, so the acceleration of gravity there is

(9.8 m/s²) · (6371 / 6971)²  =  8.2 m/s².

So the object's weight is (8.2 M) Newtons.

This is about 84% of its weight on Earth's surface.

(Notice that the astronauts aboard the International Space Station are NOT "weightless". The strength of gravity up there where they are is around 84% of what it is down on the ground.  The question of why they float, and why their muscles waste away, is a topic for another question.)