It is quite surprising that they are not comfortable in the middle station of life. It may be that they have weak characters or not ready to face the world. They can ofcourse make use of their social upliftment for their social and moral advantage but instead they redicule it.
Class has nothing to do with these characters because I find them as weak characters. Anyone in the place of Mr. Doolittle would have been much happier and so also in the place of Miss Eliza. But they can also be defended by the fact that they recently got upgraded in their social level and being new they fear or are not yet experienced to handle their present position.