Special treatment of youngest member of a group
I'm not aware of any special technical term for such a phenomenon, though colloquially the youngest child may sometimes be called "the baby of the family".  Furthermore, I'm not aware of this phenomenon existing outside of family dynamics - it might be just your personal experience.  In the workplace for example, the youngest members of a team may be treated as inexperienced or incompetent, as competition or threat, or as subordinate or servant.  Favouritism may equally be shown to the eldest, most senior, most productive, or most visionary members of a team.

Within families, a number of surveys have suggested that parents do appear to favour their youngest children.  However, a few interpretations of this phenomenon are possible.  One interpretation is that younger children demand and respond to preferential treatment over their older siblings (eg, Jensen &amp; McHale, 2017).  Another is that younger children are easier to manage than older children, and in fact they receive no better treatment than their older siblings did at the same age (eg, Mumsnet, 2018).  It is also possible that there is a cuteness effect:


  ... human adults react positively to infants who are stereotypically cute.


Also of note: Being the youngest child does not grant any special advantage later in life.