The log doesn't list everything that goes on in the game; many kinds of events are not recorded. That could explain what you're seeing with Juro's health. Also, if you have games in more than one player slot (which doesn't seem likely in your situation), villagers with the same name, but in different games, can make interpreting the log a little challenging.

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One of the babies was born with their health down a bit. Guess he got dropped on his head in the delivery room.

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I've noticed that most of the time, when they go from baby to toddler, their health bar isn't all the way up. Don't know why. Maybe the stress of being weaned, needing to eat solid food, etc. The bar always goes all the way up very quick though. :]

I only get concerned when a villager is sick. I've noticed, at least with my scenarios, villagers tend to recover (bar all the way up) on their own.

I've only got a single doctor and my villagers have only been ill a handful of times. I don't tend to worry about them unless it actually states they are sick -- they'll slowly heal on their own if you're not making them work constantly. Would you like it if you had to work 24/7?

How do you heal in real life? Bed rest. You can't force a sprained ankle to be good again. You just have to look after people's needs and wait for them to heal.