If gravity puts a force of 3n an object, how much force would it put on an second object that was twice as heavy

What we call "heaviness" is almost always the object's weight, and
that weight is exactly the force of gravity pulling the object and the Earth
together. 

So an object that's twice as heavy as 3 Newtons is an object whose weight
is twice as much as 3 N  =  6 newtons .