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Gonna have to disagree just on this point. Unless you're worried about sinking into soft ground or something, two wheels can take the weight just as well as four. Fewer wheels is often more maneuverable and there's less friction. I mean, you specifically mention wheelbarrows which show this trade off; stability for easier rolling/maneuverability.
Yeah no doubt but OP said this in reference to "scaling up with more weight" and in reference to moving things around, so there are practical size limitations on how long the wheelbarrow/lever can be and how much a person's arms can lift. You wouldn't use a wheelbarrow to move a pallet of stone without custom building some freakishly large pallet moving wheelbarrow to act as a massive lever, but you could certainly move a little bit of stone at a time with a store bought wheelbarrow. Assuming normal size implements, for the pallet, a person isn't strong enough to not need four wheels. You might make a very long lever with the right balance and be able to lift the stone pallet and move it a few feet at a time, before resetting the fulcrum and moving the load again, a few more feet, and you could move the load with just one finger, easily, as you suppose, but in no way would it be more practical than using a four-wheel pallet jack of normal size. I'm not a physics guy so I'm sure I'm not explaining this as clearly as someone more versed might and I agree there are times when it's easier to pull, such as pulling a dolly up a flight of stairs or over curb; I guess I'm assuming we're talking about moving a load along the average ground where you can get the proper angle.
For OP, check the Worx Aerocart, 8 in 1.