Not just weight though but bulk too Richard.
Back to the original question the best complete kit has to be the caldera cone. You buy the one for the pot you want to use or you can get the keg set for either Heinnekan or Fosters can. This has the cone, burner, pot made out of the beer can with lid, measuring cup, pot cosy, silicone bands (so you don't burn your lips drinking from the pot), measuring cup, fuel bottle and caddy. The pot and burner and windshield weighs 77g on its own. With all the other bits it is 183g but the main thing is it all packs into the caddy which is about 2/3rds the size of a 1 litre nalgene bottle. As far as I am concerned pack size and fuel efficiency are important as well as weight. I know the trangia kit is a nice system and works but to my mind the caldera cone is more efficient as a system. I guess if you don't have to carry the system then you can have whatever you want as weight and bulk is not a problem but if you are carrying it (backpacking or as a brew kit on day walks) then to my mind the caldera cone is a system that is hard to beat. Cue arguments about not being durable and other arguments. There will always be trangia fans and I am one but still find it is a bulky, weighty and over specced as a simple brew kit when out and about.
BTW if the original poster wants to define best brew kit as well it might help. Is it a kit to make a brew for yourself when out on a walk or something to make a load of teas for a group? From the above answers most are thinking it is a brew kit for you or at most a limited number. If you are looking for something for a larger group then trangia and the lightweight alternatives are probably not best. When I was out with BTCV groups we used a gas ring with a large kettle. Another BTCV group used a larger Kelly-kettle. Both worked well at getting a large amount of water to the boil for a group but obviously not portable (wasn't a problem as we worked from a minibus or land rover anyway).