Heaviness, weight, is variable, depending upon--among other things--the mass at the bottom of the gravity well.
It would be more accurate to ask regarding the mass of asteroids, but that is equally unanswerable. Asteroids vary in size from microscopic to minor planetoids.
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The weight of an asteroid can vary widely depending on its size. Small asteroids could weigh as little as a few hundred kilograms, while larger asteroids can weigh millions of tons. This weight is influenced by the asteroid's composition and density.
it can be up to thousands or maybe millions of pounds it depends how big the asteroid is and some parts of an asteroid is cut up to soome piesces that can weight like 20 pounds
The weight of an asteroid can vary greatly depending on its size and composition. Smaller asteroids can weigh only a few kilograms, while larger ones can weigh several billion kilograms. For example, the asteroid Ceres, which is the largest object in the asteroid belt, has an estimated weight of around 939 trillion kilograms.
Asteroids can vary in size from a few meters to hundreds of kilometers in diameter. Some asteroids are small, like pebbles, while others are quite large and can even be classified as dwarf planets. Size is one of the factors used to categorize and characterize asteroids.
Comets are Comets and Asteroids are Asteroids
An advantage of mining asteroids is that the asteroidal metals and minerals are concentrated in a small, easily accessible space and they are much purer in content.
That's hard to say, since asteroids come in all sort of sizes. By the way, it is more appropriate to talk about the mass of astronomical objects, than about their weight.