Personally I like a hatchet. There's plenty out there that are sub 3 lbs. Like any tool, it can be learned.

Unlike a saw, you can hammer with a hatchet. You can (sort of) whittle. You can use it on on a ferro rod.

And, if you need to, you can use it for self defense. You don't watch "The Patriot" and notice anyone with a pruning saw.