I don't believe weight of the gun is the weight, but actually the pull weight you wish to exert on the trigger. Greater pull weight, safer trigger, like a double action - really long first pull. Lighter weight, quicker fire time.
Hunting Rifle, one you are carrying through the woods, possibly shouldering with gloves on before taking a shot. In excess of 4# for safety.
Benchrest rifle that will be locked in place and you want the minimal disturbance prior to the shot as possible. 2 to 4 OUNCES of pressure to set it off.
As for travel of the trigger. You are talking about dwell time. The longer the trigger travel, the greater chance the barrell will wander off target prior to the round leaving the barrel.
If you have a REALLY LONG lead travel before the trigger goes bang, then you have a REALLY good chance of missing because there is a lot going on. If you have minimal travel before the trigger engages, you have less time to mess it up.