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The person saying it likes having you around and spending time with you but not alot.
"Fond of" is not a single word, therefore it is not simply one part of speech, but two. "Fond" is an adjective: "I am fond of him," or "He is my fondest friend." "Of" is a preposition, beginning prepositional phrases such as "of him," "of Alaska," or "of swimming with sharks."
Paul McCartney
"Grew fond" or "grew fond of" means the more time you spend with someone or something, the more you liked them or it.
The cast of He Was So Fond of Animals - 1913 includes: Lewin Fitzhamon as Man
Deputed Testamony Stakes was created in 1995.
Fond of Joking?. . .it's mr. bean!!
basls
Being fond of someone just means that you like the person.
fond means you have a strong like in this person as in I'm fond of john as in you like them or love them
a sesquipediophile
A blogophile is a person who is fond of blogs or blogging.
Uxorious.
epicurean
Gourmets
A fat bum. Hungry.
It means they care a lot for you. Are fond of you.