This is Kate's jacket. = This jacket belongs to Kate.
That's our neighbors' dog. = That dog belongs to our neighbors.
Belong with means that things/people are similar and should be together. If one person in a romantic relationship says "You belong with me," it is like saying that it is destiny for the two people to be together.
You can also use belong with or belong in for putting an object into a category with other, similar objects:
That book about humans traveling to Mars doesn't belong in the history section. It belongs with the other science fiction books.
An object belongs IN a category, and belongs WITH other similar things.
Body Facts
At least 1.3 billion people are infected with a small hookworm that attaches to the inside of the gut. If there are a lot, it looks like fur or a thick carpet. Around the world, they suck a total of 10 million litres (around 21 million pints) of blood a day. .. More >>