*dlegh-

The core idea of this root was:

become fixed, engage oneself, pledge allegiance

The German source I am using mainly (Dwds.de) is not mentioning this root and only traces the family to a West-Germanic word that was about “taking responsibility“, which in German later shifted toward taking care, treating well.

The English source (Etymonline.com) mentions the same West Germanic ancestor, but then traces it all the way back to this Indo-European root here.

According to Etymonline, the root is origin of

• pledge (“fixing yourself to a promise”)
• indulge (“engage oneself to”)
• play (“keep oneself busy, fixated”)