This may sound crazy, but how about filling the head with water, or maybe sand. If the inherit disadvantage of a lightweight hatchet is that it is light, then adding weight (at the camp site) should be fairly easy. I have no idea if this is practical, but I could see some sort of design involving a hollow head, with a screw on cap. Without anything in it, it would be OK (a little on the light side) but filled with water (or sand) it would be ideal.
With or without the fillable head, I think the general idea is worth pursuing (a lightweight hatchet). Yes, it may be "too light" but that just means that it is bigger. Bigger is better for chopping, right? In other words, if the thing weighs only 10 ounces, it may be the best 10 ounce hatchet around.