Mollycoddle means to spoil or overindulge something. You can think of mollycoddle as an extreme form of coddle. If you constantly fuss over your dog and serve her homemade food while she's resting on a soft feather bed, you mollycoddle her.
Mollycoddle began as a noun describing a man who pampered or indulged himself too much. When applied to men, Molly, the woman's name, was a slur meaning "too feminine." No longer just for men, the verb mollycoddle describes any kind of excessively indulgent or overprotective treatment. A coach may mollycoddle his star player by planning practice around his schedule, or you may mollycoddle your little sister by doing her homework for her when she says she's tired.