Does it really have a thinner wall or does it just appear to be thinner because since a 12-pt socket has twice as many points it doesn't have the thick wall where the flat is located? I bet if you mike them you'll find they both have the same outside diameter.
Which also leads to the question if a 6-pt socket is actually stronger than a 12-pt. since the wall thickness at the point may well be the very same. A 6-pt socket will obviously have more "grip" on the flat of the nut or bolt head which is why they are much less likely to round off the points on either nuts or bolt heads.
