I agree, the lightest deodorant is none.
That said, if you want the lightest weight antiperspirant or deodorant, that carries well and gives at least a few days of protection, then I suggest you use one of the crystal deodorants. I just break off a small chunk and put it in a mini ziplock and carry it in my toiletry kit.
For those unfamiliar with using a crystal, you wet it lightly with water to apply it. Each application can last up to 3 days, unless you bathe or shower in between.
You can find them in most health/natural stores or the toiletry sections of drug stores, or Walmart type places. They come in both regular or travel size.