To be fond of someone: I’m really fond of him”. - expresses that you like the person but also something softer. Like there is a warmth about how you feel about that person because of time shared. Similarly with being fond of something: you really enjoy doing it, seeing it, eating it. To me its invoking a sense of warmth and likeness to a subject or person. But also, a memory or nostalgia attached. Like is very generic. You like something and it’s not specific how much but you like it. Less warmth and nostalgia unless you say it with lots of intent “I really like playing this because it makes me happy”

Hello :) If you are fond of something it usually describes your hobbies, for example: I'm fond of vollayball. When you like something, it can be literally everything: I like eating pizza. I like playing football.