Tell someone "Suit yourself" when:
- you've tried to offer them something but they won't accept it
- you've tried to convince them of something, but they don't agree
"Suit yourself" means "I think you're making a bad choice, but do whatever you want." Here's an example:
A: Why don't you let me carry some of those bags for you?
B: No, I've got it.
A: OK, suit yourself.
"Suit yourself" sounds a little annoyed, but not too rude.