Sea hammocks probably had provisions for stretching them uniformly. But relying on trees in the field is problematical. I have tried them but don't like them. They were the savior to the navy, before the hammock the sailors slept on the decks with rats roaming over them. I believe they were a New World innovation and lasted through at least WW2 in the British Navy.
I didn't like them in SE Asia in the woods because they required a pretty limited choice for trees to string them, they were hard to get out of if fired upon, and they hung at grazing fire level if you got contact at night. Plus they disagreed with my back. No one in the field used hammocks except Viet Namese REMFs.
I don't know how they were used in Colonial America for ground forces, but I'm not confident they were popular for much of the same reasons above. Plus, I think they were cold. And I think because they were elevated and horizontal, they were obvious as an encampment when this wasn't desired.