"fondness" is a form of "liking" in which you also have affection. "fondness" comes mainly from the heart. "like" is a simpler, more neutral word. e.g. I don't see my little nephew much but I am very fond of him and enjoy seeing him when I can.
"keenness" is about interest and enthusiasm though has three main slightly different senses;
a) I am keen on tennis (I like tennis and take an interest in it)
b) I am keen on that girl (I am interested in getting to know her and have a relationship with her)
c) I am keen to start the presentation (I am ready and almost impatient to start it)
Kind regards, Michael