Question

Since all objects are ‘weightless’ for an astronaut in orbit, is it possible for astronauts to tell whether an object is heavy or light? Think about it, think of newton’s laws, the equations and then explain your reasoning.

Answer 1

W=gm
where g - gravitation 
m - mass
w - weight
as gravitation equals to zero, multiplying by 0 gives W=0
It is not possible to tell whether and object is heavy or light 

Answer 2

Well, while they're in orbit, nothing is 'heavy' and nothing is 'light'.
They're all weightless.

I think you're really asking:  Can the astronaut tell which objects will be
heavy and which ones will be light if they go back down to Earth ?

The answer is a resounding 'Sure' !

The weight of an object on Earth is (its mass) x (acceleration of gravity).
So the objects with a lot of mass will be heavy, and the objects with less
mass will be lighter.

How can the astronaut determine the mass of the object hanging there
in the air in front of him ? 
All he has to do is give it a push.  It'll accelerate away from him (and he
will accelerate away from the object). 
Newton's 2nd law tells us that  F=mA, so the acceleration will be

                             (the force he exerts) / (the mass).

An object with small mass will zip away from him, and it'll be light
down on the surface. 

An object with large mass will accelerate slightly, start moving slowly,
and it'll be heavy down on the surface.