2 things...
As for the mercy killings of our beloved poultry, I think I am doing my critters a favor when I relieve thier suffering and I hope someone loves and respects me enough to do the same for me if I was in that condition. I will nurse anything back to health, but it has to be able to get better and have desire to do so. If they are suffering, I make the call. I am sorry to hear of your loss. It is a deeply personal thing to be the caretaker of critters, I adore mine too.
And I should have been more clear about the weasle and the head thing. Just about everything will eat the head first, that's not what I'm talking about. Other predators will kill the chicken in some other way, you will find other trauma to the body. A weasle will only kill a chicken by popping the head off.
If you think about it this way: a weasle is too small to kill an adult chicken by any other way. Comically small, I think! hehe. But, a weasle has really sharp teeth and is wily enough to get to the sweet spot (neck). There, you have the popped head! All they do is nibble the neck and drink some blood and come back tomorrow for more (sometimes they will chew on the body a bit).
Everything else will kill the chicken in some other way. You will find a bruised body, eviscerated bowls and organs, gnawed legs, missing head, or some other sign. A weasle can not do any of those things.
An owl can walk into your coop at night, if the door is open, and will pop off heads too. However, you will find evidence of other trauma to the body. The beak and tallons of an owl are very sharp and will leave marks. A raccoon will pop the heads off several birds for fun in one night and only snack on the bodies or eviscerate them. But they leave more trauma to the body than a graceful, and tiny weasle. Raccoons are not small and not graceful when butchering chickens!
Your dogs should deter the raccoons at night if they are allowed out. Weasles will not be bothered by the dogs unless they have a particular skill for hunting weasles (and the weasles know that).