What is the difference between "Suit yourself" and "Have it your way?" Thanks?

Nothing. Both are an indication the speaker has now shut off any further input from the person they're talking to.

Suit yourself is older, it was a phrase used by Kipling in 1897. OLD meaning was --- Origin: In the old days, if someone said "suit yourself" it would mean to put on your own clothing (that you own) instead of going to a tailor and getting a new one made..

Have it your way isn't anywhere near as old. It means the same thing today as the other phrase.

There is no difference.