The feeling of weightlessness or the feeling of weighing heavier is due to the force that acts on you from the floor.
Now, if a lift is going upward with an acceleration $a$, then the weight of a man inside it will experience a weight of:
$$F = ma$$
where $F$ is the net force acting on the man and $a$ is the net acceleration of the man (and lift of course).
The force that gravity exerts on the man is given by $F_g = mg$
The net force, $F$, is obtained from the difference of the force acting on the man from the floor of the lift (which we are interested in), and the force of gravity:
$$F_{floor} - Fg = F$$
so that:
$$F_{floor} = ma + mg = m(a+g)$$
Therefore, when the lift is going up, you feel as though there is an acceleration of $(a+g)$ acting on you (I think that the $(a-g)$ in your question was a typo and should be $(a+g)$, since you feel heavier when a lift is going down and lighter when the lift is going down).
If the lift is going up at an acceleration $g$, then you feel an acceleration of $(g+g)$.
Now, to feel weightlessness, the lift has to have a certain acceleration value downwards. If this downward acceleration is equal to $g$, we get (we substitute $a$ with $-g$):
$$F_{floor} = m(-g+g) = 0$$
So that you don't feel the force the floor is acting on you and are said to be free falling.