Don't scrutinize my post if you don't even know what fireweaving is as that was the main topic of my post. Telling the OP not to listen to me is pretty rude also. OP always fireweave the last Fire in your AF3 rotation if you can. I personally use Surecast and Lethargy to fireweave. Doing this you won't ever need to transpose, and if you do get a fire 3. You lose the same time transposing as you would have done fire weaving. But you gain less DPS from a Fire 3 AF1 than a Fire 3 AF3.

Any decent BLM guide will tell you to fireweave. You don't fireweave every single fire, but fireweaving the last fire brings you into a situation where you get a Fire 3 in AF3 instead of in UI3 or AF1.