I knew the answer to this at one time. I was thinking it made a difference of 4-8 ozs. I keep thinking it was up near the 8, but that seems like a lot. I have had Remingtons with both barrel styles and could tell a big difference. The light contours just seem to point better and do not seem near as muzzle heavy. The overall barrel configuration is enough different that if you put a standard barrel on a gun that came with a light contour the forearm needs to be opened up or replaced with one for a regular barrel. On the flip side I put a light contour barrel on an old 870 and there is a pretty good gap between the barrel and forearm.
If I remember right when Remington finally went to choke tubes they beefed up the whole barrel but people did not really like the heavy gun and heavy muzzle so they changed the barrel and the light contour was born.
