Learn English – “On” vs. “at” vs. “to” in this sentence

You are right; it is not necessary. However, it's not grammatically incorrect.

Most of the time, I wouldn't use at when expressing my age. However I can imagine myself in an occasional dialogue that goes something like this:

My knees seem to ache more and more all the time nowadays.
Yes, it's rough getting old. Say, how old are you, anyway?
Me? I'm at 44.

In this context, the person is giving their age as though they are telling where they are in long race:

I'm at Mile 13; I'm halfway done with my marathon.

It's not a common usage, but it's not an incorrect one, either. Still, you are correct to say that the word at is not needed. Most of the time, I'd recommend omitting it.

You actually have the question backward! :) ... you should be asking When does an Indirect Object require a preposition?

(For those unfamiliar with the term, an Indirect Object is a secondary object of a transitive verb: it designates the entity which receives the Direct Object or for whose benefit the action is performed on the Direct Object.)

Subject - Verb - Indirect Object - Direct Object

This construction is the standard order in all di-transitive situations—those in which the verb takes both an Indirect Object and a Direct Object.

I told the police my story. OR I told them my story. I gave my son a bicycle. OR I gave him a bicycle.
I built my niece a treehouse. OR I built her a treehouse.

Sometimes, however, the Indirect Object has to fall after the Direct Object. When that happens, the syntactic relationships are no longer clear, so the Indirect Object is ‘marked’ with a preposition. There are two circumstances when this happens:

• When the Direct Object is a single pronoun it is too ‘light’ for its role to be clear, so it is moved immediately after the verb:

  ^∗ I told the police it. → ^okI told it to the police.
  ^∗ I gave my son it. → ^okI gave it to my son.
  ^∗ I built my niece it. → ^okI built it for my niece.

• When the Indirect Object is ‘heavy’, more than a couple-three words long, it draws focus for too long and it makes it difficult to recognize the Direct object, so it is moved after the Direct Object:

  ^∗ I told the police who came after I called 911 my story.→ ^okI told my story to the police who came after I called 911.
  ^∗ I gave Richard, my ten-year-old son going to school just a few blocks away, a bicycle. → ^okI gave a bicycle to Richard, my ten-year-old son going to school just a few blocks away.
  ^∗ I built my niece, my sister's daughter Lily, a treehouse. → ^okI built a treehouse for my niece, my sister's daughter Lily.

  These ‘heavy’ Indirect Objects may not seem all that hard to process; but that is because you are encountering them in writing, where you have the advantages punctuation to clarify structure and of seeing the entire sentence at once. In speech, where your hearer must process your sentence as it emerges, it isn’t so easy, and these constructions are driven by speech patterns.

Two general “rules” are operating here.

• The first is that we like to keep the core constituents of a sentence—the Subject, Verb, Indirect Object and Direct Object—as close together as possible. That drives ‘heavy’ constituents towards the right end of the sentence, where their length provides the least interruption.

• The second is that we like to put the ‘new’ information in a sentence at the right end. That drives pronouns towards the left, because pronouns are almost always ‘old’ information—they usually refer to entities which have already been introduced.