Well they could just be getting old.That is one way they are weakened.They can also be sick.If they are sick they usually go closer to the grave site or the water well.If they are sick you get one of the well villagers to learn doctoring and she/he will administer to the sick.I have taken my weakened villagers over to the food and made them eat until their meter went up.(that is the red bar at the top of the detail screen)It is very time consuming,but if you don't want then to die I suggest you do that.Someone else might know something easier than this,but that is what works for me.
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You cannot do a kindness too soon, for you never know how soon it will be too late.