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Dote
Exaggerated Affection
Use 'dote' to describe a level of affection that is visibly excessive and sometimes overwhelming to others. 
Positive Connotation
'Dote' generally implies that the affection is positive and heartfelt, even if it's too much. 
Selective Focus
When someone dotes, it often means they focus their love or affection toward a specific person or thing. 