What is the advantage of a 3inch heel versus a 2 or 2.5?

There is no advantage and I don't know any pros who wear them. Most stick to a 2.5 or 2.75 max. Sure your legs look longer on a higher heel but it is very hard to maintain your balance. As well, I have heard several women complain that they have hurt their knees dancing in 3" heels. In my opinion, 2" heels look too flat and I only wear them if I am dancing socially for a long time or my partner is short. I like 2.5 although I do compete in shoes that are 2.75. But, they do not have the stiletto heel so I have more stability.