there is a significant issue that isn't being understood regarding trying to simply enlarge the missile.
yes, you are right, to move 5 times the payload, you need to exert 5 times the effort, this requires 5 times to fuel to maintain nominal range. to keep the issues as they appear as simple and uncomplicated as possible, this will be done one step at a time, starting with the default V-2 specs.
weight 12,500kg, warhead 980kg, fuel 8720kg, 206km max range.(have you noticed your fuel is 9 times heavier than your warhead?) the missile isn't noted individually for its weight, just the combined weight, so, 12,500-980-8720=2800kg, just for the missile.
ok, so, lets double the size of the missile, to accomodate a warhead twice as large
missile 2800kg*2=5600kg, warhead 980kg*2=1960kg, fuel 8720kg, total weight 16280kg. your thrust to weight ratio, which determines your acceleration, is now 77% of what it was. to stick to simple math, moving a mass from point A to point b requires work, this is your fuel expenditure, which we did not increase. since 8720kg can move 12,500kg a distance of 206km, it follows that it should move 16280 something approximately near 160km. we have lost range AND acceleration, this isn't good. it gets worse, your missile has a larger internal volume, which results in greater drag as it must move more air out of the way to move forward, so we have now lost speed as well, this too will reduce range and acceleration, compounding the performance losses.
but all is not lost, we can always add more fuel, after all, this missile is twice as big, and we didn't give fuel its share. in so doing, we will now weight in at 25,000kg, we have accomplished our doubling completely. and now resumes the problems. we haven't redesigned the throttle assemblies, or the fuel injectors/inputs/feeds, or the nozzle. so we aren't generating any more thrust than before, but weight twice as much now. so, on with it, we are back to 206km range thanks to increased fuel you might think, this is not so, we can't maintain the speed that gave us this range for that fuel ammount because of our increased drag, so range is still down. we weight twice what we did before reducing thrust/weight to a mere 50%, acceleration further penalised by drag as before.
but so what, we can always burn more fuel in the same time period right? it stands to reason that if we consume more energy in the same time period, we have more energy to work with, and can rectify this thrust problem!. this is true, to a point. how much of a pressure increase can your manifolds take, can your fuel pumps give you the increased flow(or should we replace them for larger more powerful models even tho they are both bigger, increasing drag when the missile is enlarged to make room, and reducing acceleration), can the fuel lines handle the newly increased pressures. suppose all of this is true, you can handle the larger pressures, then we can easily double the fuel, to burn it twice as fast and our range will remain, right? wrong, double the fuel, and you increase the weight of the missile by ALOT. but lets ignore that, there is another more pressing issue looming now. if you do double the fuel rate, can sustain the pressures and keep from exploding, then you will oxidize twice as much fuel in the same period of time, ths releases twice as much energy, this includes heat. can the metals that compose your missile handle temperatures twice as much without weakening which is really bad, or melting, which would be catastrophic?
any redneck can understand that twice as much is just that, and if it needs something, then being twice as much means it needs twice as much, so supplying twice as much will solve that problem. but Nasa doesn't eploy rednecks, they never have. if rednecks could grasp rocket science, there would still be highly gifted persons at nasa, as there is alot of complicated maths that occur there not directly related to rocketry, and the rednecks would be involved with that. Nasa employs the best and the brightest because the straight forward lets just make it bigger pilosophy fails far more often than it succeeds.
The titanic wasn't much more than a massively larger motorboat, and any idiot could build something that will float, and strap a motor to it and sit a fuel tank in it, and have a motor boat, some will even achieve some decent performance. none of these people stands much chance at getting something on the scale of titanic going, and more, at that scale, its an entirely different ballgame. And rocketry is no different.
You can't simply make it bigger and get better from that. the problems that arrise become monstrously huge faster than you approach your goals. This is why miniturisation is the godsend it is, same performance from this part, at a fraction of the size/weight. Higher temperature and strength limits allow to withstand those higher pressures/temperatures. better fuel compositions to provide greater endurance and thrust at the same volume. and so on.
All of these factors combined with significantly greater understanding of the forces at work is what lead to the Saturn-V rockets, from the early days of the V-2. Do you understand ther basic concepts of a combustion engine? if your answer is yes, then you are effectively on the same page as von Braun was with rocketry, now, could you build a 400 horsepower motor on your own, no store bought parts(tools permitted obviously), that would fit under the hood of a car? this is the leap that a few decades of intensive research and miniaturisation resulted in.
bigger is not always better.