Answer :
If you're starting from zero then and assume equal accelerations the heavier object takes more force. If they're both already moving then the heavy object takes no force to keep it going. The lighter requires a force to overcome friction.
or
if it is an ordinary floor (so there is some friction) then the 1kg box will be harder to push compared to the 2000kg box on a frictionless floor. This is because the coefficient of static friction which is basically the amount of force that will be overcome to start the box moving will be higher on a floor that has friction as compared to a floor that has no friction. The floor that has no friction will require only something to push the box so an intial force it wont matter how much this force is as there is no static or kinetic friction so the 2000kg box will move at constant velocity until a force opposes it.
Pushing a 1 kg box across a carpeted floor would require more effort.
This is because of friction. Friction is the resistance of motion from one object to another. Pushing a 1 kg box across a carpeted floor requires more effort because there is friction, unlike the 2,000 kg box.
Best of luck.