Doted on their only child.
When a grandparent absolutely adores his grandchild and lavishes attention and gifts on her, this is an example of a time when he dotes on her.
When you are old and feeble minded and mutter things that no longer make sense, this is an example of a time when you dote.
Little Bill's parents just keep doting on him.
Origin of dote
- Middle English doten
From American Heritage Dictionary of the English Language, 5th Edition
- From Old English doten; compare to Germanic dotten, "to be foolish".