Does a rocket ship go further when its heavy or light?
This will depend if by bigger you mean having a larger payload,
with the same amount of propellant, or it the payload is the same
and only the mass of propellant changes. If you have more
propellant/rocket fuel then the rocket will have more energy. The
equation E=.5mv2 (e=energy, m=mass, and v=velocity) shows that if
you have more energy then the velocity will increase. But if there
is more mass then the velocity will be less. So the question is
tough to answer with no set values as to the mass of the rocket
fuel vs the mass of the payload.
However if this is about rockets in space, where the net force
acting on the rocket during the trip is effectively zero( no
friction in space), then both rockets will go equally far, both
will go indefinitely, with one just going faster than the
other.