actually, not true
the only way that fuel accelerates an object in space is because exhaust gases are released. this creates an action-reaction pair, with the shuttle being the reaction.
so basically, you could get ANYWHERE you want to with a fraction of a seconds worth of a burn. the only other factors are the gravity from other planets. this gravity is the only thing that gives a shuttle weight, not to be confused with mass. in empty space, all shuttles would have the same weight...0
but bigger ones have more mass of course.
Agree on the issue of permanent damage, however in space you may be weightless but your ships do have both mass and inertia, you need fuel to overcome both conditions and heavier ships need both more fuel and also greater acceleration time to travel anywhere.
so no, heavier ships dont need more fuel, in fact, they would need LESS fuel because their greater mass would overcome the gravitational pull of a planet/star/whatever mroe easily.