You don't say how many days you want to go on a single canister so the question is hard to answer. Did you mean the WHOLE 2 weeks on one canister? Or did you mean the opposite – that you will get resupplied a lot? The "absolute lightest canister" would most likely be the smallest but I'm not sure this is what you are talking about.
That said, per unit volume, the Berikades are the lightest I think (also by far the most expensive). These also have the advantage that in addition to the 3 "standard" sizes they sell, because of the simple design you can also get a custom one with virtually any length/volume you would like. If weight is the only factor (not cost) then I'm thinking one of thee will be the best. The smallest is the scout (1 lb 12 oz), and they don't get smaller options because the bear is not suppose to be able to carry it.
Take a look at their site, and then think carefully what you want to do.
Another option – the bear vault solo is a little smaller and a litter heavier, but a lot cheaper. Lots of people, including me, also find them a lot more annoying to open at the end of a long day.
p.s. I think you can sit on all of the canisters. LOL