(This is a longer version of my comment on YOU’s answer.)
Let me state an objection to what seems to be a popular theory about the origin of 蝶よ花よ, which YOU also stated as (not main) part of the answer.
As YOU said, a few (actually more than a few) pages claim that the phrase 蝶よ花よ appeared in the form 花や蝶や in Makura no Sōshi (completed in 1002). However, this claim seems groundless to me.
Some of these pages even quote the poem in Makura no Sōshi which contains the phrase 花や蝶や:
みな人の花や蝶やといそぐ日もわがこころをば君ぞ知りける (みなひとの はなやちょうやと いそぐひも わがこころをば きみぞしりける) While everyone cares only about beautiful things such as flowers and butterflies, you and only you care about my heart.
In this quote, 花や蝶や describes two examples of beautiful things. But I cannot see any connection between this meaning and the phrase 蝶よ花よ which describes how a child is raised with a lot of (or even too much) affection.
So 花や蝶や in the quote above has a different order, a different particle and a different meaning from 蝶よ花よ. I find it much more reasonable to consider 花や蝶や above as unrelated from the set phrase 蝶よ花よ rather than the same phrase in a different form and usage, unless there is some evidence suggesting otherwise.
As I said, there are many pages stating this as the origin of 蝶よ花よ. But my gut feeling is that it seems that they copied this claim from somewhere (possibly without thinking). As is often the case in this kind of discussions in linguistics, the large number of pages claiming something is hardly a measure of reliability of the claim.
Neither Daijisen nor Daijirin states the origin of the phrase 蝶よ花よ. I do not have access to a larger dictionary.