Red Beard,
You are correct in that people make excellent one shot kills with light weight rifles and pistols all the time.
I hope you did not take offense to my comments. Nobody said you can't shoot well with a lighter rifle. It's all relative and if you're comfortable with your rifle, you only need to satisfy yourself.
However, everything else being equal, a heavier gun is likely to remain more stable before, during, and after squeezing the trigger. At least for that 1/24,000 of a second and 3/8" of recoil while the bullet remains in the barrel. It can be one of many factors affecting the initial shot as well as subsequent shots when shooting for groups.
Becoming proficient at long range generally requires practice. And, heavier guns, with heavier barrels, tend not to wear on some of us less than lighter ones and you don't have to wait so long for the barrel to cool.
Happy hunting,
Richard