The bansner isn't real slim, but the stock is ridiculously light. Around 24 OZ's.... It's lighter than the stock on my 270 fwt. That's just a hunters compact with the standard fill though. For shooting off the bench, the bansner is definitely more comfortable. Here's some pics to tide you over while I get some more for you:
Bansner on pre 64 338:
Bansner on classic sporter:
Factory Tupperware on classic sporter:
Honestly if you are looking for really trim at the forend, the Mcmillan hunters compact is pretty slim. If you get that with the edge fill, it's pretty light as well: