I always lifted my glass carboys by the handle, but would also try to get a hand underneath as quickly as possible for better support. It's moot, as I stopped using glass somewhat recently when I cracked a carboy (not while lifting, but nonetheless). Just not worth the risk any longer for me.
As to play in the handle, they make different size handles for different carboys. If you have an acid carboy with the narrower neck, you need a smaller handle. The smaller one that I have is brown, not orange.
The good news is that the orange handles fit perfectly on Better Bottles for when you switch over.