Why is the flow from overhead tank merely a trickle?
The way you've drawn it, during the "limited time", the static pressure at the tap is determined by the vertical distance between the tap and the water surface in the "overhead tank" and not the "storage tank". 

Outside the "limited time" the static pressure at the tap is determined by the difference in height between the tap and the water surface in the "storage tank".

Restricted flow to the tap is probably due to a blockage (or insufficient pipe diameter for length of run) somewhere in the pipework. It is possible that non-return valve NRV2 is blocked, faulty or installed incorrectly.