Obviously if you were firing a 10 Mag load of 2oz from a 7lb gun you would need more convergence than if firing a .410 oz load from a 10lb gun. That big load from the little gun is simply going to move it around more than the little load from a big gun. If you don't believe that "SHOOT" each of'em.
Barrel convergence is speaking of the mechanical alignment of the bores axis. When you are speaking of converging at 40yds, 75yds etc this is not the mechanical convergence of the bbls but where they are "Destined" to hit together.

Miller/TN
I Didn't Say Everything I Said, Yogi Berra