In my experience, the character of the trigger is more important than the weight. I have handguns with relatively light triggers that make accurate shooting difficult due to creep and overtravel and others with heavier trigger pulls that are easier to shoot well because the trigger moves smoothly, breaks cleanly and doesn't have a lot of overtravel after it breaks.
There is a point at which it becomes very difficult to shoot a handgun accurately due to a heavy trigger. What that trigger weight is depends on the hand strength of the shooter in question and his/her willingness the spend time trying to master the trigger.
Very well said ... beat me to it.
I guess I must have strong fingers because my double action revolvers (most have pulls between 10 and 14 lbs) all feel great to me. They are consistent, smooth and have a nice clean break. I had a Taurus 94 that must have had a 15+ lb pull, and would have been fine with the weight had it not been for all the lumpy, gritty crap going on in the works.
OTH, I had a 1911 with comparatively lighter SA trigger that although light, was absolutely terrible overall (very rough, lot of initial slop, jerky inconsistent release and too much over travel). I was having trouble maintaining basketball-sized groups at 7 yards with that gun, until I had it cleaned up. Now ragged one hole groups are achievable at the same distance.