Granfors Bruks makes 2 axes that work extremely well as a pair for a LOT of work, the SFA and the ... SFA.
Confusing!
The Small Forest axe is a 19 inch handle (about like your average 'hawk), with a 3.25 inch cutting face and a 1.5 pound weight.
The Scandinavian Forest Axe is very close to a traditional timber cruiser's axe-- but single bitted! It has a 3.5 inch cutting face and a 2 pound head weight on a longer 25 inch handle. While this isn't a full on lumberjack's felling axe, it does the job much better than a "camp hatchet."
Most Camp hatchets don't have the mass to work as an axe, or the geometry to work the way a chopper (knife) would. They make okay splitting wedges, but since anyone with a knife and wood can MAKE splitting wedges, why bother carrying one?
I personally wouldn't go much, if any, under 2 pounds in an axe. hawks, and the small GOOD hatchets like the hunstman, have their place and work out quite well, but they are more specialized tools. (with the caveat that I've doen a fair amount of firewood work with a french pattern hawk from a maker on BF that has enough mass and face to do the work)