It is mostly to do with color. If something is not a color singlet, gluons attach to it. Trying to separate the two quarks of a meson it is thought that a tube

It is mostly to do with color. If something is not a color singlet, gluons attach to it. Trying to separate the two quarks of a meson it is thought that a tube of gluons forms between them of which the energy is linear in the length of the tube. Since force is the derivative of energy, this leads to a constant force.