If something fits you or fits into a place, it is the right size or shape for you or for that place:
[trying on shoes in a shoe shop]
These fit perfectly. And I like the colour. I think I’ll buy them.
I’ve put on weight and my trousers don’t fit me anymore!
Will this table fit into the space between the bookshelf and the wall?
If something suits someone or something, it is right for that person or thing or situation, or it makes that person or thing look more attractive.
Wednesday at ten o’clock for the meeting suits me perfectly.
That sofa suits the room really well – the colours match the walls.
Black doesn’t suit me; I look better in lighter colours.
We don’t use fit when we mean that something is right for a person or thing or situation:
This restaurant suits people who like simple food.
Not: This restaurant fits people …