why springs get harder to compress?

There are different designs of springs, with different properties:

• Constant Force Springs - Constant Force Spring Design Theory (2nd Source)

The extension type of constant force spring represents the most basic, yet most versatile, type of constant force spring. It is a pre-stressed flat strip of spring material which is formed into virtually constant radius coils around itself or on a drum. When the strip is extended (deflected) the inherent stress resists the loading force, the same as a common extension spring, but at a nearly constant (zero) rate (change in load per unit deflection, generally given in pounds per inch).

A constant torque is obtained when the outer end of the spring is attached to another spool and caused to wind in either the reverse or same direction as it is originally wound. The full rated load of the spring is reached after being deflected to a length equal to 1.25 times its diameter. Thereafter, it maintains a relatively constant force regardless of extension length. Load (force applied to a spring that causes a deflection) is basically determined by the thickness and width of the material and the diameter of the coil.

• Compression Springs - Compression Spring Design General Considerations (2nd Source)

A compression spring is an open-coil helical spring that offers resistance to a compressive force applied axially. Compression Springs are the most common metal spring configuration and are in fact one of the most efficient energy storage devices available.

• Extension or Tension Springs - Extension Spring Design Theory (2nd Source)

Helical extension springs are similar to helical compression springs, but are loaded in tension. Hooks or loops are provided to allow a pull force to be applied. Usually, extension springs are attached at both ends to other components. When these components move apart, the spring tries to bring them together again.

• Helical or Torsion Springs - Torsion Spring Design Theory (2nd Source)

Helical springs used to apply a torque or store rotational energy are commonly referred to as torsion springs. The ends of torsion springs are attached to other components, and when those components rotate around the center of the spring, the spring tries to push them back to their original position. Although the name implies otherwise, torsion springs are subjected to bending stress rather than torsional stress. They can store and release angular energy or statically hold a mechanism in place by deflecting the legs about the body centerline axis.

Comparison of the force applied vs. amount of movement.