Perhaps you need to move an aquarium across town, or even just across the room. As you empty it, the thought pops into your head that it would be a lot easier if you just left the gravel in it, or even some of the water, and you wonder: What's the harm? It's quite possible you can successfully move a small- to medium-size tank with gravel, and even some water in it. However, I would not recommend doing it.
Never Move a Tank With Water
First things first. Moving a fragile glass box full of heavy, sloshy liquid is a recipe for disaster. Even the slightest adjustment or correction in your movement will make the water shift, throwing off the load—and likely your back. This will surely be followed by an instinctive reflex on your part to try to prevent spilling the water, making matters worse. You'd be crazy to move a completely full tank, and since you're draining some of the water anyway (because you're not crazy), it's stupid not to drain it all (and of course you're also not stupid).
Don't Stress the Seals
While leaving the gravel and even some of the water in the aquarium might not break it, the seals will be placed under uneven stress. Today's sealants are extremely good at holding the aquarium glass together, but they aren't designed to withstand sheer forces. Sheer force occurs when there is uneven pressure—like twisting or diagonal pressure—put on the seals.
A tank that is sitting on a well-supported, level surface does not experience stress on the seals. But when the tank is moved, the motion can put uneven pressure on those seals. If the tank is empty, that stress is not enough to cause a problem. But if the tank has additional weight from substrate or water, the stress created by moving the tank can break a seal.
The damaged seal might not be apparent until the tank is filled and later begins to leak. This risk is significant enough that most aquarium manufacturers will void the warranty on their product if it is moved with anything in it. For that reason alone, I advise emptying your aquarium before moving it.
If You Do It Anyway
I confess that I have moved partially filled aquariums, particularly with small inexpensive tanks. But I knew I was taking a risk. I don't think I would do it again, as it’s far easier to empty the tank up front than to replace it later because it leaks.
If you're just moving the tank across the room—and choosing to ignore the above advice—there are ways to do this as sensibly as possible. Remove all or at least most of the water from the tank, transferring it to clean plastic buckets or tubs. If possible, keep the tank on its original support unit (cabinet, stand, table, etc.), and move the unit and tank together, sliding the unit on moving sliders or carpet scraps (if the flooring is hard).
If must lift and move the tank, slide it onto a piece of 3/4-inch plywood (or similarly strong, flat material), and carry it on the material, with at least one helper to keep the tank level.
This will put less stress on the seals than simply moving it by hand, given the twisting forces imposed by two people walking and carrying at the same time.