You can see that if a was equal to g, your downward acceleration is that of gravity, namely the cable has snapped in the elevator, Then you don't feel any weight.
The summer months see Times Square overrun by visitors all scrambling for their "I Heart NYC" t-shirt and matching sun visor, while the Empire State Building's elevator queue can, through the heat-haze, seem to extend as far, horizontally, as the iconic building stretches for the skies.