Friction is proportional to the Normal Force

Friction occurs in two cases.  When objects are at rest relative to each other static friction opposes any tendency to slip.  When objects are sliding relative to each other kinetic friction opposes the tendency to slide relative to the surface.
The Coefficient of friction   is a constant that indicates how surfaces interact. static f ≤  μ s N   kinetic f = µ k N

FRICTION

The unit of force is the Newton!

Weight equals the force of gravity exerted by a planet on a mass.

The Normal force always acts perpendicular to the surface and points toward the object pushing against the surface.

The Normal Force is the force a surface provides when an object pushes against it.

Normal Forces ( N or Fn)   are created by the molecular bonding of the molecules of the surface.  They "push back"  when an object pushes against them.

The Concept of Force

Law of Universal Gravitation

NORMAL FORCE

One Newton is the force needed to accelerate one kilogram at the rate of one meter per second squared.

N Force

links

WEIGHT

May the Net Force be with you!
The force of gravity or weight may be calculated using    F = GmM/r² where M is the Mass of the planet. Using m as the mass of the object whose weight is being calculated, the weight also equals mg. The acceleration due to gravity yields "g" and is different on every planet. 
Apparent weight measures the normal force or the force of a scale pushing on an object.  It may or may not equal to the force of gravity.

Special Forces

Friction

Weight