Hi Walt, does the status of your sick villager actually show 'sick' or 'weakened'? A villager can only be healed if they have a status of sick. The only way to improve the helath bar if a villager is weak, is to ensure that you have plenty of food around, and try to give the villager an easier role. I usually let them do some researching. It seems that if they are doing active tasks, the extra exertion makes recovery slower, and tasks such as building can actually make it worse as well
Hope this helps, but feel free to ask if you have more questions
Savi