It sounds like a double set trigger. Such a trigger operates in two modes. The front lever is the actual trigger, the rear lever is used to "set" the trigger. Neither actually cocks the gun.
The way it works is this. The first mode is using the trigger set. You do this by pulling the rear lever until it clicks, or "cocks" the trigger mechanism. When you do this the front lever, the actual trigger, will typically be very light, going off more or less at a touch. This mode is intended for a deliberate shot when you have time, though when you get used to it you may find yourself using it more often (I've often realised, even after taking a quick running shot, that I set the trigger out of force of habit).
The other mode however, is unset. This is where you just pull the front lever, without setting the mechanism with the rear. Typically the trigger pull in this mode will be a lot heavier, and it is intended for those quick shots where you don't have time to set the trigger.
Have you tried using the trigger unset, ie without "cocking" the rear trigger?
