Hi Sarah,
When we view someone as being inferior to us, or lower in status than us, we "despise" him or her. In other words, we look down on that person.
Example: The rich millionaire despised the poor villagers who lined the streets to welcome him into their village. / I despise those adults who abuse their own children.
When we do or say something to make someone feel less important, we "belittle" that person.
Example: He belittles his co-workers by speaking to them in a condescending manner. Everyone avoids him like a plague.
Main difference is that when we despise someone, it can be a mental desposition while we physically do something (an action or use words) to belittle someone whom we despise.
Hope this helps.
Cheers,
Lance