Chibiusa's obsession with Mamoru is very similar at the core to her closeness to Usagi. Mamoru is her dear papa, only he has plenty of time to spend with her and take her to the amusement park and spoil her rotten on candy and let her sleep in his bed. Mamoru has the time to lavish the attention on Chibiusa that Endymion cannot afford, and can also be more familiar with his affections because he is not yet King of the World and Chibiusa is not yet his royal daughter.
And Chibiusa is clearly a daddy's girl in the first place, which further fuels her attachment to Mamoru. Many children have this kind of attachment with their parent of opposite gender while growing up. They eventually grow out of it, just as Chibiusa does.
Also, for a very long time Mamoru is one of the only constant forces of love in her life (outside of Usagi) with whom she can share the ups and downs of being a Sailor Soldier. She's best friends with Pluto, who dies. She's best friends with Hotaru, who becomes a baby again and is taken away. Pluto leaves again as well. Mamoru is always there to protect her, and she's often left in his care while the others are fighting. She sees Usagi as something of a rival, so it's understandable that she'd bond to Mamoru as a care-giver, especially since he seems to fit her idea of a papa better than Usagi fits into the role of mama.
Chibiusa and Mamoru also seem to have a strong power resonance, allowing him to sense things from her just by touching her, and also allowing them to combine powers, as seen in the interestingly named "Pink Sugar Tuxedo Attack" in the Snow Princess story.