On a 14-20 day trip there isn't going to be a huge weight difference between the Vargo Jet Ti, a high efficiency alcohol stove, or a good esbits system. ayce did a nice stove weight over 14 days article/gram. My experience is slightly different but are similar.
If you like using a canister stove... then by all means take it on the JMT. It will work well and be pretty hassle free. I wouldn't stress about carrying an extra 3oz (empty fuel canister).
As others have noted there are several places you can do easy resupply (at least for canister and alcohol... and I guess esbits according to someone in this thread) . The JMT is short enough not to require resupplying fuel... but my preference would be to do a resupply at Reds, Muir Ranch, or VVR for food, and while I am at it I would do fuel/canister. I am pretty sure I have seen iso butane canisters for sale at all three. I seem to recall alcohol for sale at Muir ranch, but it was at a hideous markup.
There is always the option of going stoveless. This summer I ended up going stoveless because it was going to be warm enough that I didn't want to bother cooking.