The weight of an object is a force due to gravity towards the centre of the earth.
Normally, it is perpendicular to the ground. It is fundatmental and continuous force.
About the normal force....
When you stand up, you are not pulled by the strong fundatmenal gravitional force.
According to Newton First Law, there is no net force. Obviously, that force acts against the gravitational force is the force by the ground. It is a reaction force which maintain your equillibrium and it is passive, so it is called normal force. Actually, it is a kind of electromagnetic force.
Down a slope, there is a force from the surface of that pyramid. That's the normal force. Fancy without this force, the object will go into the pyramid since there is a net force.