Is there a light-hearted word or phrase for a hypochondriac parent?

Solution 1:

A worrywart \ˈwər-ē-ˌwȯrt\ is a term which may describe a parent who worries excessively about their child's health, a person who tends to worry habitually and often needlessly.

Nervous Nelly, is perhaps the most light-hearted expression I am aware of, which describes a very fearful or nervous person . You could call a mother a "nervous Nelly mom", this doesn't necessarily describes a parent who is hypochondriac by proxy but it could include this behaviour.

many new parents are nervous Nellies when it comes to the health of their babies

And a term which I think strikes the right balance between gentle teasing and description accuracy is over-parenting.
_{Kidspot parent exchange}

OK, so we all have days where we are, like, over it, but over-parenting is another thing entirely. It's when you get too into the detail of your role as a parent that you can't see the wood for the trees.

Solution 2:

Given the clarification from the edit, here are a few less severe options:

• worrisome — tending to worry: having a tendency to worry
• overprotective
• tender — with gentle feeling: showing care, gentleness, and feeling
• with or using "kid gloves"
• precautious — using or displaying precaution

Here are two relevant terms that have some relation to your intended meaning:

helicopter parent — a parent who pays extremely close attention to a child's or children's experiences and problems, particularly at educational institutions

Helicopter parents are traditionally seen as overly worrisome or paranoid. This could certainly apply to medical concerns.

I wasn't able to find anything more specific but if you used the phrase "parental hypochondria" I suspect most English speakers would understand your intent.

One potentially relevant footnote is the term Münchausen syndrome by proxy.

Münchausen syndrome by proxy — a behavior pattern in which a caregiver deliberately exaggerates, fabricates, and/or induces physical, psychological, behavioral, and/or mental health problems in those who are in their care

Münchausen syndrome by proxy is a very complicated mental illness that is somewhat related to your desired term in the sense that the illness is through "proxy"; only instead of Münchausen syndrome you are looking for something like hypochondria.

It is worth noting that you should be careful to never confuse the two. Hypochondria is usually a worry of wellbeing while Münchausen syndrome by proxy is usually an attention seeking behavior.

Solution 3:

"Hypervigilant parent" may be as close as you can come to the term you're looking for.

Granted, hypervigilance is a state of sensory arousal common in patients with PTSD, it is also used to describe parents who are always concerned with potential illness in children, and is thought by some to contribute to hypochondriasis.

One can be an over-attached parent, a fretful parent, or simply anxious parent.

There was a phrase we used to use to describe the anxiety of a parent whose child had a very serious illness, and due to this illness tended to be overly fretful, but this, it would seem, is not the situation you are describing.

Solution 4:

Perhaps not the precise term you are seeking but one closely related is to 'mollycoddle', one meaning of which is 'to treat indulgently, or overprotectively'. (Oxford Dictionary of English)