Use it to show you're stepping back and letting someone else decide, despite your own opinion. Alright, go ahead with the blue paint then, have it your own way!
Pro Tip 2/3
Subtle Disagreement
It carries an undertone of disagreement or skepticism about the other person's choice. You're really going to write the whole essay tonight? Have it your own way!
Pro Tip 3/3
Colloquial Tone
It's casual speech, more suitable for conversations with friends or family, not formal settings. This isn't how I'd pack a suitcase, but have it your own way.