Question: What do we mean by the term [weight](https://en.wikipedia.org/wiki/Weight)? Is it an upward force exerted by an object to counteract the downward force of gravity (or) is it the downward force itself? Is the magnitude of the weight always equal to the gravitational force regardless of the frame?

Answer: 
It is a consequence of the 3rd law. The man pushes down on the floor, with his weight, and the floor pushes back with an equal and opposite normal force.
Weight is defined as *[the force with which the body is acting on its support or the suspension](https://en.wikipedia.org/wiki/Weight#Operational_definition)*, whereas the normal force is the force with which the support acts on the body. (Note that this is different from what is understood by *weight* in everyday life - the measure of gravitational mass.)

Depending on a situation these may or may not form a 3rd law couple:

* If a block rests on a horizontal surface, the weight and the normal force form the third law couple
* On an inclined surface, the weight is composed of the force counteracting the normal force and the friction force
* Adding a supsension to either of the above two cases may further complicate the situation.