Hatchets are heavy and bulky. I have a couple I carry for muzzleloading and camp.
The small one is a H&B Forge Squaw Hawk and the large one is a JT Forge English F&I War issue.
A better choice, IMHO, is a Finnish leuku knife and a ratchet pruner. Lighter, smaller, multi-use.
The upper knife is an 8" leuku (by Puukkojunkkari) and will lop a 1" branch with a single strike. (The lower is current Finnish army issue and a sweet blade). Great combo for hunting and camp. 1095 steel and Rockwell 60 to 62.
Add a pair of lightweight Fiskar pruners and you can quietly and easily build camp, make kindling, build a ground blind or clear a shooting lane.