Meaning of あばば in あばばをしてみせる


I am reading _Not of Color_ by Sawako Ariyoshi (有吉佐和子『非色』) at the moment. I
came across this paragraph detailing how the protagonist takes care of her
newborn baby, Mary:

>
> 一年というもの、私の朝夕はメアリイと共に明け暮れたと言っていい。ＰＸの買物の殆どはトムがしたし、母は来ると掃除とアイロンかけを手伝ってくれ、終わると早々に帰って行く。そこで私だけがメアリイにお座りをさせ、
> **[あばば]{﹅﹅﹅}をしてみせ** 、メアリイの表情の変化を素早く読んでお尻をさっぱりさせてやった。（河出文庫 p.55）

The word あばば has an emphasis mark attached to it. I could not find this entry
in several dictionaries. The closest I could find online was 『あばばばば』 by
Ryūnosuke Akutagawa, with the following explanation I took from [another Q&A
site](https://detail.chiebukuro.yahoo.co.jp/qa/question_detail/q1359439283):

> 語源は、赤ん坊をあやす時の「いないいないバア」のような「あばばばばぁ～」です｡

Meaning it is something said when calming a baby. I would like to know

  * if this is a correct explanation of あばば in the 『非色』 excerpt too;
  * if there is any particular reason あばば was emphasised; and
  * how exactly the verb してみせる functions in this context.




  * if this is a correct explanation of あばば in the 『非色』 excerpt too;

Yes, it is. To me, it is kind of oldish to call it あばば, it is now commonly
referred to as いないいないばあ. Not only is it said, but it is _done_. See [the video
of this page](https://www2.shimajiro.co.jp/happy085/fureai/haihai.html), for
example. Basically you cup and disclose your face to attract the attention of
child.

  * if there is any particular reason あばば was emphasised; and

I think it is more for clarifying that あばば is a single word than emphasizing.
The same usage explained in [this chiebukuro
answer](https://detail.chiebukuro.yahoo.co.jp/qa/question_detail/q12172024727).

> 仮名で書かれているので読みにくいために、＜一つのことば＞として区別できるようにしています。

  * how exactly the verb してみせる functions in this context.

してみせる literally means _do and show_. あばば here is considered as a movement
rather than the phrase itself, so the sentence is saying _I did (and showed)
the movement of あばば to Mary_.




  * if this is a correct explanation of あばば in the 『非色』 excerpt too;

Yes, it is. To me, it is kind of oldish to call it あばば, it is now commonly
referred to as いないいないばあ. Not only is it said, but it is _done_. See [the video
of this page](https://www2.shimajiro.co.jp/happy085/fureai/haihai.html), for
example. Basically you cup and disclose your face to attract the attention of
child.

  * if there is any particular reason あばば was emphasised; and

I think it is more for clarifying that あばば is a single word than emphasizing.
The same usage explained in [this chiebukuro
answer](https://detail.chiebukuro.yahoo.co.jp/qa/question_detail/q12172024727).

> 仮名で書かれているので読みにくいために、＜一つのことば＞として区別できるようにしています。

  * how exactly the verb してみせる functions in this context.

してみせる literally means _do and show_. あばば here is considered as a movement
rather than the phrase itself, so the sentence is saying _I did (and showed)
the movement of あばば to Mary_.

