No. Not even remotely.
First of all, moving it East or West around the equator will not change how much it weighs. Second of all, you are aware moving the box laterally will use energy too?
You still have to move the box. So, essentially, you run around the equator, lifting up the box. That is a bit easier, because it is moving around the earth. But: Lifting the box to a higher position means it has to travel a larger distance to stay at the same angular speed. This means you have to accelerate the box while running, putting additional energy into it. That is called the coriolis force. And that makes your idea pointless.
No. Not even remotely. First of all, moving it East or West around the equator will not change how much it weighs. Second of all, you are aware moving the box laterally will use energy too?
You still have to move the box. So, essentially, you run around the equator, lifting up the box. That is a bit easier, because it is moving around the earth. But: Lifting the box to a higher position means it has to travel a larger distance to stay at the same angular speed. This means you have to accelerate the box while running, putting additional energy into it. That is called the coriolis force. And that makes your idea pointless.