Bottom Navigation Bar: Text size is increasing on pressing?

Try to add this code in dimens.xml file

<dimen name="design_bottom_navigation_text_size" tools:override="true">10sp</dimen>
<dimen name="design_bottom_navigation_active_text_size" tools:override="true">10sp</dimen>

You can set the active and inactive textAppearance for a BottomNavigationView via styles:

<android.support.design.widget.BottomNavigationView
    android:id="@+id/navigation"
    android:layout_width="match_parent"
    android:layout_height="wrap_content"
    style="@style/BottomNavigationView"/>

Put below styles in styles.xml file

<style name="BottomNavigationView">
    <item name="itemTextAppearanceActive">@style/TextAppearance.BottomNavigationView.Active</item>
    <item name="itemTextAppearanceInactive">@style/TextAppearance.BottomNavigationView.Inactive</item>
</style>

 <!-- blank styles for better code readability-->
<style name="TextAppearance"/>
<style name="TextAppearance.BottomNavigationView"/>

<!-- inactive tab icon style -->
<style name="TextAppearance.BottomNavigationView.Inactive">
    <item name="android:textSize">12sp</item>
</style>

<!-- active tab icon style -->
<style name="TextAppearance.BottomNavigationView.Active">
    <item name="android:textSize">12sp</item>
</style>

With TextAppearance you can control more than just textSize, but also properties such as fontFamily, etc.