How can two magnets demonstrate magnetic force?
A simple two-pan scale demonstrates gravitational force when you show that two different objects have the same mass. First you place an unknown mass on one side of the scale. Then you add known masses to the other side until the scale reaches its balance point. Gravity is acting with the same force on both sides of the scale.
Think of trying the same thing with a magnetic force. Place one magnet on one pan of the scale with the poles oriented vertically. Then balance the scale by adding mass to the other side. This mass is is proportion to the gravitational force on the magnet. Next, place the second magnet under the scale (directly below the first magnet with poles oriented vertically) and rebalance.
If you placed the two magnets so that opposite poles are facing each other, the force will be attractive and you will need to add more mass to the opposite side of the scale. If the facing poles are the same, the force is repulsive and acts against gravity. You may need to remove mass from the other side. It might even be necessary to add mass to the side with the magnet.
By noting the difference in the mass before before and after introducing the external magnetic field you can calculate the force between the two magnets at this distance.
In principle, the force between two magnets can be measured much the same way one measures the gravitational force between an object the earth. As a practical application, the measurement may be a little more difficult. You'll need a scale with no ferromagnetic parts. The strength of a small dipole magnet changes quickly as a function of distance. If you get the magnets too near each other, one may flip over or they may suddenly slam together.