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Inspired by this puzzle

I am a common word that refers to a person.
I often refer to very young people – in fact, the younger a person is, the more likely they are to be called me.
However, if you pick two random siblings, the older of them is more likely than the younger one to be called me.

I believe the answer is:

Junior

This is because:

While Junior may be a nickname for anyone young, it is a generational title that is more commonly bestowed upon the eldest child. Thus, it is more likely for (e.g.) Fred Senior (the father) to have his firstborn son named Fred Junior, and any other sons named 'not-Fred' than for the 'Junior' to be bestowed upon a younger son.

I am a common word that refers to a person.
I often refer to very young people – in fact, the younger a person is, the more likely they are to be called me.

I believe the word is

Baby -- the younger someone is the more likely they are to be called baby

However, if you pick two random siblings, the older of them is more likely than the younger one to be called me.

But if you take two random siblings, the older one is likely to start dating sooner than the younger. A common term of endearment for a significant other is Baby. So the older sibling would be more likely to be called baby than their younger sibling... assuming neither of them are actual babies...

That could be...

Heir (or next in line, etc)

Because obviously...

Given two siblings, the older one is more likely to be the heir. But the older he/she is, the more likely it is that their predecessor has already passed away, in which case they have already inherited whatever title or property they had to, and (usually) are not called "heir" anymore.

I am a common word that refers to a person.

A child

I often refer to very young people.

Children are very young.

In fact, the younger a person is, the more likely they are to be called me.

Again, children are very young.

However, if you pick two random siblings, the older of them is more likely than the younger one to be called me.

If you pick two random siblings, the younger one could be a baby and the older one could still be a child

I thought about this a million times and another answer could be:

A teen

Although I doubt I'm right. :D

Perhaps

Sibling

Because

Children are often referred to as sibling or brother or sister. As in "he is so and so's sibling". When you get older you are referred to that less commonly (often defined by other relationships). However, a first child is not a sibling until a second one gets born, so when still young there's a higher chance that they don't have younger siblings.

I think following can be answer for:

" I often refer to very young people – in fact, the younger a person is, the more likely they are to be called me"

Bachelor

Because some older persons calls themselves by this status to claim that they are younger!

"However, if you pick two random siblings, the older of them is more likely than the younger one to be called me."

Obviously older sibling will get this status earlier